#!/usr/bin/perl -w
# Copyright 2010, 2011, 2012, 2013, 2014, 2015, 2016 Kevin Ryde
# This file is part of Math-PlanePath.
#
# Math-PlanePath is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the Free
# Software Foundation; either version 3, or (at your option) any later
# version.
#
# Math-PlanePath is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
# for more details.
#
# You should have received a copy of the GNU General Public License along
# with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.
# cf A094605 rule 30 period of nth diagonal
# A094606 log2 of that period
#
use 5.004;
use strict;
use Test;
use List::Util 'min';
plan tests => 199;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
use Math::PlanePath::CellularRule;
# uncomment this to run the ### lines
# use Smart::Comments '###';
sub streq_array {
my ($a1, $a2) = @_;
if (! ref $a1 || ! ref $a2) {
return 0;
}
while (@$a1 && @$a2) {
if ($a1->[0] ne $a2->[0]) {
MyTestHelpers::diag ("differ: ", $a1->[0], ' ', $a2->[0]);
return 0;
}
shift @$a1;
shift @$a2;
}
return (@$a1 == @$a2);
}
#------------------------------------------------------------------------------
# duplications
foreach my $elem (# [ 'A071030', 'A118109', 'rule=54' ],
# [ 'A071033', 'A118102', 'rule=94' ],
# [ 'A071036', 'A118110', 'rule=150' ],
[ 'A071037', 'A118172', 'rule=158' ],
[ 'A071039', 'A118111', 'rule=190' ],
) {
my ($anum1, $anum2, $name) = @$elem;
my ($aref1) = MyOEIS::read_values($anum1);
my ($aref2) = MyOEIS::read_values($anum2);
$#$aref1 = min($#$aref1, $#$aref2);
$#$aref2 = min($#$aref1, $#$aref2);
my $str1 = join(',', @$aref1);
my $str2 = join(',', @$aref2);
print "$name ", $str1 eq $str2 ? "same" : "different","\n";
if ($str1 ne $str2) {
print " $str1\n";
print " $str2\n";
}
}
#------------------------------------------------------------------------------
# A061579 - permutation N at -X,Y
MyOEIS::compare_values
(anum => 'A061579',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::CellularRule->new (n_start => 0, rule => 50);
my @got;
for (my $n = $path->n_start; @got < $count; $n++) {
my ($x, $y) = $path->n_to_xy ($n);
push @got, $path->xy_to_n (-$x,$y);
}
return \@got;
});
#------------------------------------------------------------------------------
# A262867 Total number of ON (black) cells after n iterations of the "Rule 153" elementary cellular automaton starting with a single ON (black) cell.
# A263511 Total number of ON (black) cells after n iterations of the "Rule 155" elementary cellular automaton starting with a single ON (black) cell.
# A263807 Total number of ON (black) cells after n iterations of the "Rule 157" elementary cellular automaton starting with a single ON (black) cell.
# A265205 Number of ON cells in the n-th iteration of the "Rule 73" elementary cellular automaton starting with a single ON cell.
# A265206 Total number of ON cells after n iterations of the "Rule 73" elementary cellular automaton starting with a single ON cell.
# A265219 Number of OFF (white) cells in the n-th iteration of the "Rule 73" elementary cellular automaton starting with a single ON (black) cell.
# A265220 Total number of OFF (white) cells after n iterations of the "Rule 73" elementary cellular automaton starting with a single ON (black) cell.
# A265223 Total number of OFF (white) cells after n iterations of the "Rule 150" elementary cellular automaton starting with a single ON (black) cell.
# A265224 Total number of OFF (white) cells after n iterations of the "Rule 30" elementary cellular automaton starting with a single ON (black) cell.
# A265225 Total number of ON (black) cells after n iterations of the "Rule 54" elementary cellular automaton starting with a single ON (black) cell.
# A265283 Number of ON (black) cells in the n-th iteration of the "Rule 94" elementary cellular automaton starting with a single ON (black) cell.
# A265284 Total number of ON (black) cells after n iterations of the "Rule 94" elementary cellular automaton starting with a single ON (black) cell.
# A265321 Total number of ON (black) cells after n iterations of the "Rule 110" elementary cellular automaton starting with a single ON (black) cell.
# A265322 Number of OFF (white) cells in the n-th iteration of the "Rule 110" elementary cellular automaton starting with a single ON (black) cell.
# A265323 Total number of OFF (white) cells after n iterations of the "Rule 110" elementary cellular automaton starting with a single ON (black) cell.
# A265382 Total number of ON (black) cells after n iterations of the "Rule 158" elementary cellular automaton starting with a single ON (black) cell.
# A265428 Number of ON (black) cells in the n-th iteration of the "Rule 188" elementary cellular automaton starting with a single ON (black) cell.
# A265429 Total number of ON (black) cells after n iterations of the "Rule 188" elementary cellular automaton starting with a single ON (black) cell.
# A265430 Number of OFF (white) cells in the n-th iteration of the "Rule 188" elementary cellular automaton starting with a single ON (black) cell.
# A265431 Total number of OFF (white) cells after n iterations of the "Rule 188" elementary cellular automaton starting with a single ON (black) cell.
# A267880 Decimal representation of the middle column of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.
# A267881 Number of ON (black) cells in the n-th iteration of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.
# A267882 Total number of ON (black) cells after n iterations of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.
# A267883 Number of OFF (white) cells in the n-th iteration of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.
# A267884 Total number of OFF (white) cells after n iterations of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.
# A267872 Number of ON (black) cells in the n-th iteration of the "Rule 237" elementary cellular automaton starting with a single ON (black) cell.
# A267873 Number of ON (black) cells in the n-th iteration of the "Rule 235" elementary cellular automaton starting with a single ON (black) cell.
# A267874 Total number of ON (black) cells after n iterations of the "Rule 235" elementary cellular automaton starting with a single ON (black) cell.
# A267682 Total number of ON (black) cells after n iterations of the "Rule 201" elementary cellular automaton starting with a single ON (black) cell.
# A267610 Total number of OFF (white) cells after n iterations of the "Rule 182" elementary cellular automaton starting with a single ON (black) cell.
# A267590 Number of ON (black) cells in the n-th iteration of the "Rule 169" elementary cellular automaton starting with a single ON (black) cell.
# A267591 Total number of ON (black) cells after n iterations of the "Rule 169" elementary cellular automaton starting with a single ON (black) cell.
# A267592 Number of OFF (white) cells in the n-th iteration of the "Rule 169" elementary cellular automaton starting with a single ON (black) cell.
# A267593 Total number of OFF (white) cells after n iterations of the "Rule 169" elementary cellular automaton starting with a single ON (black) cell.
# A267582 Number of ON (black) cells in the n-th iteration of the "Rule 167" elementary cellular automaton starting with a single ON (black) cell.
# A267583 Total number of ON (black) cells after n iterations of the "Rule 167" elementary cellular automaton starting with a single ON (black) cell.
# A267528 Number of ON (black) cells in the n-th iteration of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell.
# A267529 Total number of ON (black) cells after n iterations of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell.
# A267530 Number of OFF (white) cells in the n-th iteration of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell.
# A267531 Total number of OFF (white) cells after n iterations of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell.
# A267516 Number of ON (black) cells in the n-th iteration of the "Rule 137" elementary cellular automaton starting with a single ON (black) cell.
# A267517 Total number of ON (black) cells after n iterations of the "Rule 137" elementary cellular automaton starting with a single ON (black) cell.
# A267518 Number of OFF (white) cells in the n-th iteration of the "Rule 137" elementary cellular automaton starting with a single ON (black) cell.
# A267519 Total number of OFF (white) cells after n iterations of the "Rule 137" elementary cellular automaton starting with a single ON (black) cell.
# A267458 Number of ON (black) cells in the n-th iteration of the "Rule 133" elementary cellular automaton starting with a single ON (black) cell.
# A267459 Total number of ON (black) cells after n iterations of the "Rule 133" elementary cellular automaton starting with a single ON (black) cell.
# A267460 Number of OFF (white) cells in the n-th iteration of the "Rule 133" elementary cellular automaton starting with a single ON (black) cell.
# A267461 Total number of OFF (white) cells after n iterations of the "Rule 133" elementary cellular automaton starting with a single ON (black) cell.
# A267451 Number of ON (black) cells in the n-th iteration of the "Rule 131" elementary cellular automaton starting with a single ON (black) cell.
# A267452 Total number of ON (black) cells after n iterations of the "Rule 131" elementary cellular automaton starting with a single ON (black) cell.
# A267453 Number of OFF (white) cells in the n-th iteration of the "Rule 131" elementary cellular automaton starting with a single ON (black) cell.
# A267454 Total number of OFF (white) cells after n iterations of the "Rule 131" elementary cellular automaton starting with a single ON (black) cell.
# A267445 Number of ON (black) cells in the n-th iteration of the "Rule 129" elementary cellular automaton starting with a single ON (black) cell.
# A267446 Total number of ON (black) cells after n iterations of the "Rule 129" elementary cellular automaton starting with a single ON (black) cell.
# A267447 Number of OFF (white) cells in the n-th iteration of the "Rule 129" elementary cellular automaton starting with a single ON (black) cell.
# A267448 Total number of OFF (white) cells after n iterations of the "Rule 129" elementary cellular automaton starting with a single ON (black) cell.
# A267368 Total number of ON (black) cells after n iterations of the "Rule 126" elementary cellular automaton starting with a single ON (black) cell.
# A267369 Total number of OFF (white) cells after n iterations of the "Rule 126" elementary cellular automaton starting with a single ON (black) cell.
# A267352 Number of ON (black) cells in the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell.
# A267353 Total number of ON (black) cells after n iterations of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell.
# A267354 Number of OFF (white) cells in the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell.
# A267259 Number of ON (black) cells in the n-th iteration of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell.
# A267260 Total number of ON (black) cells after n iterations of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell.
# A267261 Number of OFF (white) cells in the n-th iteration of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell.
# A267262 Total number of OFF (white) cells after n iterations of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell.
# A267212 Total number of ON (black) cells after n iterations of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.
# A267214 Total number of OFF (white) cells after n iterations of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.
# A267159 Total number of ON (black) cells after n iterations of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell.
# A267161 Total number of OFF (white) cells after n iterations of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell.
# A267149 Total number of ON (black) cells after n iterations of the "Rule 105" elementary cellular automaton starting with a single ON (black) cell.
# A267151 Total number of OFF (white) cells after n iterations of the "Rule 105" elementary cellular automaton starting with a single ON (black) cell.
# A267047 Total number of ON (black) cells after n iterations of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.
# A267049 Total number of OFF (white) cells after n iterations of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.
# A266899 Total number of ON (black) cells after n iterations of the "Rule 75" elementary cellular automaton starting with a single ON (black) cell.
# A266901 Total number of OFF (white) cells after n iterations of the "Rule 75" elementary cellular automaton starting with a single ON (black) cell.
my @data =
(
# Not quite, initial values differ
# [ 'A051341', 7, 'bits' ],
# A080513 Number of ON (black) cells in the n-th iteration of the "Rule 70" elementary cellular automaton starting with a single ON (black) cell.
#
# A226463 Triangle read by rows giving successive states of cellular automaton generated by "Rule 135".
# A226464 Triangle read by rows giving successive states of cellular automaton generated by "Rule 149".
# A226482 Number of runs of consecutive ones and zeros in successive states of cellular automaton generated by "Rule 30".
#
# A265688 Binary representation of the n-th iteration of the "Rule 190" elementary cellular automaton starting with a single ON (black) cell.
# A265695 Triangle read by rows giving successive states of cellular automaton generated by "Rule 135" initiated with a single ON (black) cell.
# A265696 Binary representation of the n-th iteration of the "Rule 135" elementary cellular automaton starting with a single ON (black) cell.
# A265697 Decimal representation of the n-th iteration of the "Rule 135" elementary cellular automaton starting with a single ON (black) cell.
# A265698 Middle column of the "Rule 135" elementary cellular automaton starting with a single ON (black) cell.
# A265699 Binary representation of the middle column of the "Rule 135" elementary cellular automaton starting with a single ON (black) cell.
# A265700 Decimal representation of the middle column of the "Rule 135" elementary cellular automaton starting with a single ON (black) cell.
# A265701 Number of ON (black) cells in the n-th iteration of the "Rule 135" elementary cellular automaton starting with a single ON (black) cell.
# A265702 Total number of ON (black) cells after n iterations of the "Rule 135" elementary cellular automaton starting with a single ON (black) cell.
# A265703 Number of OFF (white) cells in the n-th iteration of the "Rule 135" elementary cellular automaton starting with a single ON (black) cell.
# A265704 Total number of OFF (white) cells after n iterations of the "Rule 135" elementary cellular automaton starting with a single ON (black) cell.
# A265715 Binary representation of the n-th iteration of the "Rule 149" elementary cellular automaton starting with a single ON (black) cell.
# A265717 Decimal representation of the n-th iteration of the "Rule 149" elementary cellular automaton starting with a single ON (black) cell.
# A265718 Triangle read by rows giving successive states of cellular automaton generated by "Rule 1" initiated with a single ON (black) cell.
# A265720 Binary representation of the n-th iteration of the "Rule 1" elementary cellular automaton starting with a single ON (black) cell.
# A265721 Decimal representation of the n-th iteration of the "Rule 1" elementary cellular automaton starting with a single ON (black) cell.
# A265722 Number of ON (black) cells in the n-th iteration of the "Rule 1" elementary cellular automaton starting with a single ON (black) cell.
# A265723 Number of OFF (white) cells in the n-th iteration of the "Rule 1" elementary cellular automaton starting with a single ON (black) cell.
# A265724 Total number of OFF (white) cells after n iterations of the "Rule 1" elementary cellular automaton starting with a single ON (black) cell.
# A266068 Binary representation of the n-th iteration of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.
# A266069 Decimal representation of the n-th iteration of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.
# A266070 Middle column of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.
# A266071 Binary representation of the middle column of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.
# A266072 Number of ON (black) cells in the n-th iteration of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.
# A266073 Number of OFF (white) cells in the n-th iteration of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.
# A266074 Total number of OFF (white) cells after n iterations of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.
# A266090 Decimal representation of the n-th iteration of the "Rule 17" elementary cellular automaton starting with a single ON (black) cell.
# A266155 Triangle read by rows giving successive states of cellular automaton generated by "Rule 19" initiated with a single ON (black) cell.
# A266174 Triangle read by rows giving successive states of cellular automaton generated by "Rule 5" initiated with a single ON (black) cell.
# A266175 Binary representation of the n-th iteration of the "Rule 5" elementary cellular automaton starting with a single ON (black) cell.
# A266176 Decimal representation of the n-th iteration of the "Rule 5" elementary cellular automaton starting with a single ON (black) cell.
# A266178 Triangle read by rows giving successive states of cellular automaton generated by "Rule 6" initiated with a single ON (black) cell.
# A266179 Binary representation of the n-th iteration of the "Rule 6" elementary cellular automaton starting with a single ON (black) cell.
# A266180 Decimal representation of the n-th iteration of the "Rule 6" elementary cellular automaton starting with a single ON (black) cell.
# A266216 Triangle read by rows giving successive states of cellular automaton generated by "Rule 7" initiated with a single ON (black) cell.
# A266217 Binary representation of the n-th iteration of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.
# A266218 Decimal representation of the n-th iteration of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.
# A266219 Binary representation of the middle column of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.
# A266220 Number of ON (black) cells in the n-th iteration of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.
# A266221 Total number of ON (black) cells after n iterations of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.
# A266222 Number of OFF (white) cells in the n-th iteration of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.
# A266223 Total number of OFF (white) cells after n iterations of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.
# A266243 Triangle read by rows giving successive states of cellular automaton generated by "Rule 9" initiated with a single ON (black) cell.
# A266244 Binary representation of the n-th iteration of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.
# A266245 Decimal representation of the n-th iteration of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.
# A266246 Middle column of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.
# A266247 Binary representation of the middle column of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.
# A266248 Decimal representation of the middle column of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.
# A266249 Number of ON (black) cells in the n-th iteration of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.
# A266250 Total number of ON (black) cells after n iterations of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.
# A266251 Number of OFF (white) cells in the n-th iteration of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.
# A266252 Total number of OFF (white) cells after n iterations of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.
# A266253 Triangle read by rows giving successive states of cellular automaton generated by "Rule 11" initiated with a single ON (black) cell.
# A266254 Binary representation of the n-th iteration of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.
# A266255 Decimal representation of the n-th iteration of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.
# A266256 Number of ON (black) cells in the n-th iteration of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.
# A266257 Total number of ON (black) cells after n iterations of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.
# A266258 Number of OFF (white) cells in the n-th iteration of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.
# A266259 Total number of OFF (white) cells after n iterations of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.
# A266282 Triangle read by rows giving successive states of cellular automaton generated by "Rule 13" initiated with a single ON (black) cell.
# A266283 Binary representation of the n-th iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell.
# A266284 Decimal representation of the n-th iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell.
# A266285 Number of ON (black) cells in the n-th iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell.
# A266286 Number of OFF (white) cells in the n-th iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell.
# A266287 Total number of OFF (white) cells after n iterations of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell.
# A266298 Triangle read by rows giving successive states of cellular automaton generated by "Rule 14" initiated with a single ON (black) cell.
# A266299 Binary representation of the n-th iteration of the "Rule 14" elementary cellular automaton starting with a single ON (black) cell.
# A266300 Triangle read by rows giving successive states of cellular automaton generated by "Rule 15" initiated with a single ON (black) cell.
# A266301 Binary representation of the n-th iteration of the "Rule 15" elementary cellular automaton starting with a single ON (black) cell.
# A266302 Decimal representation of the n-th iteration of the "Rule 15" elementary cellular automaton starting with a single ON (black) cell.
# A266303 Number of ON (black) cells in the n-th iteration of the "Rule 15" elementary cellular automaton starting with a single ON (black) cell.
# A266304 Total number of OFF (white) cells after n iterations of the "Rule 15" elementary cellular automaton starting with a single ON (black) cell.
# A266323 Binary representation of the n-th iteration of the "Rule 19" elementary cellular automaton starting with a single ON (black) cell.
# A266324 Decimal representation of the n-th iteration of the "Rule 19" elementary cellular automaton starting with a single ON (black) cell.
# A266326 Triangle read by rows giving successive states of cellular automaton generated by "Rule 20" initiated with a single ON (black) cell.
# A266327 Binary representation of the n-th iteration of the "Rule 20" elementary cellular automaton starting with a single ON (black) cell.
# A266377 Triangle read by rows giving successive states of cellular automaton generated by "Rule 21" initiated with a single ON (black) cell.
# A266379 Binary representation of the n-th iteration of the "Rule 21" elementary cellular automaton starting with a single ON (black) cell.
# A266380 Decimal representation of the n-th iteration of the "Rule 21" elementary cellular automaton starting with a single ON (black) cell.
# A266381 Binary representation of the n-th iteration of the "Rule 22" elementary cellular automaton starting with a single ON (black) cell.
# A266382 Decimal representation of the n-th iteration of the "Rule 22" elementary cellular automaton starting with a single ON (black) cell.
# A266383 Total number of ON (black) cells after n iterations of the "Rule 22" elementary cellular automaton starting with a single ON (black) cell.
# A266384 Total number of OFF (white) cells after n iterations of the "Rule 22" elementary cellular automaton starting with a single ON (black) cell.
# A266434 Triangle read by rows giving successive states of cellular automaton generated by "Rule 23" initiated with a single ON (black) cell.
# A266435 Binary representation of the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.
# A266436 Decimal representation of the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.
# A266437 Number of ON (black) cells in the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.
# A266438 Total number of ON (black) cells after n iterations of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.
# A266439 Number of OFF (white) cells in the n-th iteration of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.
# A266440 Total number of OFF (white) cells after n iterations of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.
# A266441 Triangle read by rows giving successive states of cellular automaton generated by "Rule 25" initiated with a single ON (black) cell.
# A266442 Binary representation of the n-th iteration of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
# A266443 Decimal representation of the n-th iteration of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
# A266444 Middle column of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
# A266445 Binary representation of the middle column of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
# A266446 Decimal representation of the middle column of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
# A266447 Number of ON (black) cells in the n-th iteration of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
# A266448 Total number of ON (black) cells after n iterations of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
# A266449 Number of OFF (white) cells in the n-th iteration of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
# A266450 Total number of OFF (white) cells after n iterations of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
# A266459 Triangle read by rows giving successive states of cellular automaton generated by "Rule 27" initiated with a single ON (black) cell.
# A266460 Binary representation of the n-th iteration of the "Rule 27" elementary cellular automaton starting with a single ON (black) cell.
# A266461 Decimal representation of the n-th iteration of the "Rule 27" elementary cellular automaton starting with a single ON (black) cell.
# A266502 Triangle read by rows giving successive states of cellular automaton generated by "Rule 28" initiated with a single ON (black) cell.
# A266508 Binary representation of the n-th iteration of the "Rule 28" elementary cellular automaton starting with a single ON (black) cell.
# A266514 Triangle read by rows giving successive states of cellular automaton generated by "Rule 29" initiated with a single ON (black) cell.
# A266515 Binary representation of the n-th iteration of the "Rule 29" elementary cellular automaton starting with a single ON (black) cell.
# A266516 Decimal representation of the n-th iteration of the "Rule 29" elementary cellular automaton starting with a single ON (black) cell.
# A266588 Triangle read by rows giving successive states of cellular automaton generated by "Rule 37" initiated with a single ON (black) cell.
# A266589 Binary representation of the n-th iteration of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.
# A266590 Decimal representation of the n-th iteration of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.
# A266591 Middle column of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.
# A266592 Binary representation of the middle column of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.
# A266593 Number of ON (black) cells in the n-th iteration of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.
# A266594 Total number of ON (black) cells after n iterations of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.
# A266595 Number of OFF (white) cells in the n-th iteration of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.
# A266596 Total number of OFF (white) cells after n iterations of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.
# A266605 Triangle read by rows giving successive states of cellular automaton generated by "Rule 39" initiated with a single ON (black) cell.
# A266606 Binary representation of the n-th iteration of the "Rule 39" elementary cellular automaton starting with a single ON (black) cell.
# A266607 Decimal representation of the n-th iteration of the "Rule 39" elementary cellular automaton starting with a single ON (black) cell.
# A266608 Triangle read by rows giving successive states of cellular automaton generated by "Rule 41" initiated with a single ON (black) cell.
# A266609 Binary representation of the n-th iteration of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
# A266610 Decimal representation of the n-th iteration of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
# A266611 Middle column of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
# A266612 Binary representation of the middle column of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
# A266613 Decimal representation of the middle column of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
# A266614 Number of ON (black) cells in the n-th iteration of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
# A266615 Total number of ON (black) cells after n iterations of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
# A266616 Number of OFF (white) cells in the n-th iteration of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
# A266617 Total number of OFF (white) cells after n iterations of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
# A266619 Triangle read by rows giving successive states of cellular automaton generated by "Rule 45" initiated with a single ON (black) cell.
# A266621 Binary representation of the n-th iteration of the "Rule 45" elementary cellular automaton starting with a single ON (black) cell.
# A266622 Decimal representation of the n-th iteration of the "Rule 45" elementary cellular automaton starting with a single ON (black) cell.
# A266623 Middle column of the "Rule 45" elementary cellular automaton starting with a single ON (black) cell.
# A266624 Binary representation of the middle column of the "Rule 45" elementary cellular automaton starting with a single ON (black) cell.
# A266625 Decimal representation of the middle column of the "Rule 45" elementary cellular automaton starting with a single ON (black) cell.
# A266626 Number of ON (black) cells in the n-th iteration of the "Rule 45" elementary cellular automaton starting with a single ON (black) cell.
# A266627 Total number of ON (black) cells after n iterations of the "Rule 45" elementary cellular automaton starting with a single ON (black) cell.
# A266628 Number of OFF (white) cells in the n-th iteration of the "Rule 45" elementary cellular automaton starting with a single ON (black) cell.
# A266629 Total number of OFF (white) cells after n iterations of the "Rule 45" elementary cellular automaton starting with a single ON (black) cell.
# A266659 Triangle read by rows giving successive states of cellular automaton generated by "Rule 47" initiated with a single ON (black) cell.
# A266660 Binary representation of the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.
# A266661 Decimal representation of the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.
# A266662 Number of ON (black) cells in the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.
# A266663 Total number of ON (black) cells after n iterations of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.
# A266664 Number of OFF (white) cells in the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.
# A266665 Total number of OFF (white) cells after n iterations of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.
# A266666 Triangle read by rows giving successive states of cellular automaton generated by "Rule 51" initiated with a single ON (black) cell.
# A266667 Binary representation of the n-th iteration of the "Rule 51" elementary cellular automaton starting with a single ON (black) cell.
# A266668 Decimal representation of the n-th iteration of the "Rule 51" elementary cellular automaton starting with a single ON (black) cell.
# A266669 Triangle read by rows giving successive states of cellular automaton generated by "Rule 53" initiated with a single ON (black) cell.
# A266670 Binary representation of the n-th iteration of the "Rule 53" elementary cellular automaton starting with a single ON (black) cell.
# A266671 Decimal representation of the n-th iteration of the "Rule 53" elementary cellular automaton starting with a single ON (black) cell.
# A266672 Triangle read by rows giving successive states of cellular automaton generated by "Rule 57" initiated with a single ON (black) cell.
# A266673 Binary representation of the n-th iteration of the "Rule 57" elementary cellular automaton starting with a single ON (black) cell.
# A266674 Decimal representation of the n-th iteration of the "Rule 57" elementary cellular automaton starting with a single ON (black) cell.
# A266678 Middle column of the "Rule 175" elementary cellular automaton starting with a single ON (black) cell.
# A266680 Binary representation of the middle column of the "Rule 175" elementary cellular automaton starting with a single ON (black) cell.
# A266716 Triangle read by rows giving successive states of cellular automaton generated by "Rule 59" initiated with a single ON (black) cell.
# A266717 Binary representation of the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
# A266718 Decimal representation of the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
# A266719 Middle column of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
# A266720 Binary representation of the middle column of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
# A266721 Decimal representation of the middle column of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
# A266722 Number of ON (black) cells in the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
# A266723 Total number of ON (black) cells after n iterations of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
# A266724 Number of OFF (white) cells in the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
# A266725 Total number of OFF (white) cells after n iterations of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
# A266752 Binary representation of the n-th iteration of the "Rule 163" elementary cellular automaton starting with a single ON (black) cell.
# A266753 Decimal representation of the n-th iteration of the "Rule 163" elementary cellular automaton starting with a single ON (black) cell.
# A266754 Triangle read by rows giving successive states of cellular automaton generated by "Rule 165" initiated with a single ON (black) cell.
# A266786 Triangle read by rows giving successive states of cellular automaton generated by "Rule 61" initiated with a single ON (black) cell.
# A266787 Binary representation of the n-th iteration of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
# A266788 Decimal representation of the n-th iteration of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
# A266789 Middle column of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
# A266790 Binary representation of the middle column of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
# A266791 Decimal representation of the middle column of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
# A266792 Number of ON (black) cells in the n-th iteration of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
# A266793 Total number of ON (black) cells after n iterations of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
# A266794 Number of OFF (white) cells in the n-th iteration of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
# A266795 Total number of OFF (white) cells after n iterations of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
# A266809 Binary representation of the n-th iteration of the "Rule 62" elementary cellular automaton starting with a single ON (black) cell.
# A266810 Decimal representation of the n-th iteration of the "Rule 62" elementary cellular automaton starting with a single ON (black) cell.
# A266811 Total number of ON (black) cells after n iterations of the "Rule 62" elementary cellular automaton starting with a single ON (black) cell.
# A266813 Total number of OFF (white) cells after n iterations of the "Rule 62" elementary cellular automaton starting with a single ON (black) cell.
[ 'A266837', 67, 'bits' ],
[ 'A266838', 67, 'bignum', base=>2 ],
[ 'A266839', 67, 'bignum' ],
[ 'A266840', 69, 'bits' ],
[ 'A266841', 69, 'bignum', base=>2 ],
[ 'A266842', 69, 'bignum' ],
[ 'A266843', 70, 'bits' ],
[ 'A266844', 70, 'bignum', base=>2 ],
[ 'A266846', 70, 'bignum' ],
[ 'A071022', 70, 'bits', part=>'left' ],
[ 'A266848', 71, 'bits' ],
[ 'A266849', 71, 'bignum', base=>2 ],
[ 'A266850', 71, 'bignum' ],
[ 'A266892', 75, 'bits' ],
[ 'A266893', 75, 'bignum', base=>2 ],
[ 'A266894', 75, 'bignum' ],
[ 'A266895', 75, 'bits', part => 'centre' ],
[ 'A266896', 75, 'bignum_central_column' ],
[ 'A266897', 75, 'bignum_central_column', base=>2 ],
[ 'A266900', 75, 'number_of', value=>0 ],
[ 'A266898', 75, 'number_of', value=>1 ],
[ 'A266872', 77, 'bignum', base=>2 ],
[ 'A266873', 77, 'bignum' ],
[ 'A266974', 78, 'bits' ],
[ 'A266975', 78, 'bignum', base=>2 ],
[ 'A266976', 78, 'bignum' ],
[ 'A266977', 78, 'number_of', value=>1 ],
[ 'A266978', 79, 'bits' ],
[ 'A266979', 79, 'bignum', base=>2 ],
[ 'A266980', 79, 'bignum' ],
[ 'A266981', 79, 'number_of', value=>1 ],
[ 'A266982', 81, 'bits' ],
[ 'A266983', 81, 'bignum', base=>2 ],
[ 'A266984', 81, 'bignum' ],
[ 'A267001', 83, 'bits' ],
[ 'A267002', 83, 'bignum', base=>2 ],
[ 'A267003', 83, 'bignum' ],
[ 'A267006', 84, 'bits' ],
[ 'A267034', 85, 'bits' ],
[ 'A267035', 85, 'bignum', base=>2 ],
[ 'A267036', 85, 'bignum' ],
[ 'A265280', 86, 'bignum', base=>2 ],
[ 'A265281', 86, 'bignum' ],
[ 'A267037', 89, 'bits' ],
[ 'A267038', 89, 'bignum', base=>2 ],
[ 'A267039', 89, 'bignum' ],
[ 'A265172', 90, 'bignum', base=>2 ],
[ 'A267015', 91, 'bits' ],
[ 'A267041', 91, 'bignum', base=>2 ],
[ 'A267042', 91, 'bignum' ],
[ 'A267043', 91, 'bits', part => 'centre' ],
[ 'A267044', 91, 'bignum_central_column' ],
[ 'A267045', 91, 'bignum_central_column', base=>2 ],
[ 'A267048', 91, 'number_of', value=>0 ],
[ 'A267046', 91, 'number_of', value=>1 ],
[ 'A267050', 92, 'bits' ],
[ 'A267051', 92, 'bignum', base=>2 ],
[ 'A267052', 92, 'bignum' ],
[ 'A267053', 93, 'bits' ],
[ 'A267054', 93, 'bignum', base=>2 ],
[ 'A267055', 93, 'bignum' ],
[ 'A267056', 97, 'bits' ],
[ 'A267057', 97, 'bignum', base=>2 ],
[ 'A267058', 97, 'bignum' ],
[ 'A267126', 99, 'bits' ],
[ 'A267127', 99, 'bignum', base=>2 ],
[ 'A267128', 99, 'bignum' ],
[ 'A267129', 101, 'bits' ],
[ 'A267130', 101, 'bignum', base=>2 ],
[ 'A267131', 101, 'bignum' ],
[ 'A265319', 102, 'bignum', base=>2 ],
[ 'A267136', 103, 'bits' ],
[ 'A267138', 103, 'bignum', base=>2 ],
[ 'A267139', 103, 'bignum' ],
[ 'A267145', 105, 'bits' ],
[ 'A267146', 105, 'bignum', base=>2 ],
[ 'A267147', 105, 'bignum' ],
[ 'A267150', 105, 'number_of', value=>0 ],
[ 'A267148', 105, 'number_of', value=>1 ],
[ 'A267152', 107, 'bits' ],
[ 'A267153', 107, 'bignum', base=>2 ],
[ 'A267154', 107, 'bignum' ],
[ 'A267155', 107, 'bits', part => 'centre' ],
[ 'A267156', 107, 'bignum_central_column' ],
[ 'A267157', 107, 'bignum_central_column', base=>2 ],
[ 'A267160', 107, 'number_of', value=>0 ],
[ 'A267158', 107, 'number_of', value=>1 ],
[ 'A243566', 109, 'bits' ],
[ 'A267206', 109, 'bignum', base=>2 ],
[ 'A267207', 109, 'bignum' ],
[ 'A267208', 109, 'bits', part => 'centre' ],
[ 'A267209', 109, 'bignum_central_column' ],
[ 'A267210', 109, 'bignum_central_column', base=>2 ],
[ 'A267213', 109, 'number_of', value=>0 ],
[ 'A267211', 109, 'number_of', value=>1 ],
[ 'A265320', 110, 'bignum', base=>2 ],
[ 'A267253', 111, 'bits' ],
[ 'A267254', 111, 'bignum', base=>2 ],
[ 'A267255', 111, 'bignum' ],
[ 'A267256', 111, 'bits', part => 'centre' ],
[ 'A267257', 111, 'bignum_central_column' ],
[ 'A267258', 111, 'bignum_central_column', base=>2 ],
[ 'A267269', 115, 'bits' ],
[ 'A267270', 115, 'bignum', base=>2 ],
[ 'A267271', 115, 'bignum' ],
[ 'A267272', 117, 'bits' ],
[ 'A267273', 117, 'bignum', base=>2 ],
[ 'A267274', 117, 'bignum' ],
[ 'A267275', 118, 'bignum', base=>2 ],
[ 'A267276', 118, 'bignum' ],
[ 'A267292', 121, 'bits' ],
[ 'A267293', 121, 'bignum', base=>2 ],
[ 'A267294', 121, 'bignum' ],
[ 'A267349', 123, 'bits' ],
[ 'A267350', 123, 'bignum', base=>2 ],
[ 'A267351', 123, 'bignum' ],
[ 'A267355', 124, 'bits' ],
[ 'A267356', 124, 'bignum', base=>2 ],
[ 'A267357', 124, 'bignum' ],
[ 'A267358', 125, 'bits' ],
[ 'A267359', 125, 'bignum', base=>2 ],
[ 'A267360', 125, 'bignum' ],
[ 'A071035', 126, 'bits' ],
[ 'A267364', 126, 'bignum', base=>2 ],
[ 'A267365', 126, 'bignum' ],
[ 'A267366', 126, 'bignum_central_column' ],
[ 'A267367', 126, 'bignum_central_column', base=>2 ],
[ 'A267417', 129, 'bits' ],
[ 'A267440', 129, 'bignum', base=>2 ],
[ 'A267441', 129, 'bignum' ],
[ 'A267442', 129, 'bits', part => 'centre' ],
[ 'A267443', 129, 'bignum_central_column' ],
[ 'A267444', 129, 'bignum_central_column', base=>2 ],
[ 'A267418', 131, 'bits' ],
[ 'A267449', 131, 'bignum', base=>2 ],
[ 'A267450', 131, 'bignum' ],
[ 'A267423', 133, 'bits' ],
[ 'A267456', 133, 'bignum', base=>2 ],
[ 'A267457', 133, 'bignum' ],
[ 'A267463', 137, 'bits' ],
[ 'A267511', 137, 'bignum', base=>2 ],
[ 'A267512', 137, 'bignum' ],
[ 'A267513', 137, 'bits', part => 'centre' ],
[ 'A267514', 137, 'bignum_central_column' ],
[ 'A267515', 137, 'bignum_central_column', base=>2 ],
[ 'A267520', 139, 'bits' ],
[ 'A267523', 139, 'bignum', base=>2 ],
[ 'A267524', 139, 'bignum_central_column' ],
[ 'A267525', 141, 'bits' ],
[ 'A267526', 141, 'bignum', base=>2 ],
[ 'A267527', 141, 'bignum' ],
[ 'A267533', 143, 'bits' ],
[ 'A267535', 143, 'bignum', base=>2 ],
[ 'A267536', 143, 'bignum' ],
[ 'A267537', 143, 'bits', part => 'centre' ],
[ 'A267538', 143, 'bignum_central_column' ],
[ 'A267539', 143, 'bignum_central_column', base=>2 ],
[ 'A262805', 145, 'bits' ],
[ 'A262860', 145, 'bignum' ],
[ 'A262859', 145, 'bignum', base=>2 ],
[ 'A262808', 147, 'bits' ],
[ 'A262862', 147, 'bignum' ],
[ 'A262861', 147, 'bignum', base=>2 ],
[ 'A262864', 147, 'bignum_central_column', base=>2 ],
[ 'A262863', 147, 'bignum_central_column' ],
[ 'A265246', 149, 'bits' ],
[ 'A262866', 153, 'bignum' ],
[ 'A262855', 153, 'bits' ],
[ 'A262865', 153, 'bignum', part => 'centre', base=>2 ],
[ 'A263243', 155, 'bits' ],
[ 'A263244', 155, 'bignum', base=>2 ],
[ 'A263245', 155, 'bignum' ],
[ 'A263804', 157, 'bits' ],
[ 'A263805', 157, 'bignum', base=>2 ],
[ 'A263806', 157, 'bignum' ],
[ 'A265379', 158, 'bignum', base=>2 ],
[ 'A265380', 158, 'bignum_central_column' ],
[ 'A265381', 158, 'bignum_central_column', base=>2 ],
[ 'A263919', 163, 'bits' ],
[ 'A267246', 165, 'bignum', base=>2 ],
[ 'A267247', 165, 'bignum' ],
[ 'A267576', 167, 'bits' ],
[ 'A267577', 167, 'bignum', base=>2 ],
[ 'A267578', 167, 'bignum' ],
[ 'A267579', 167, 'bits', part => 'centre' ],
[ 'A267580', 167, 'bignum_central_column' ],
[ 'A267581', 167, 'bignum_central_column', base=>2 ],
[ 'A264442', 169, 'bits' ],
[ 'A267585', 169, 'bignum', base=>2 ],
[ 'A267586', 169, 'bignum' ],
[ 'A267587', 169, 'bits', part => 'centre' ],
[ 'A267588', 169, 'bignum_central_column' ],
[ 'A267589', 169, 'bignum_central_column', base=>2 ],
[ 'A267594', 173, 'bits' ],
[ 'A267595', 173, 'bignum', base=>2 ],
[ 'A267596', 173, 'bignum' ],
[ 'A265186', 175, 'bits' ],
[ 'A262779', 175, 'bignum', base=>2 ],
[ 'A267604', 175, 'bignum_central_column', base=>2 ],
[ 'A267598', 177, 'bits' ],
[ 'A267599', 177, 'bignum', base=>2 ],
[ 'A267605', 181, 'bits' ],
[ 'A267606', 181, 'bignum', base=>2 ],
[ 'A267607', 181, 'bignum' ],
[ 'A267608', 182, 'bignum', base=>2 ],
[ 'A267609', 182, 'bignum' ],
[ 'A267612', 185, 'bits' ],
[ 'A267613', 185, 'bignum', base=>2 ],
[ 'A267614', 185, 'bignum' ],
[ 'A267621', 187, 'bits' ],
[ 'A267622', 187, 'bignum', base=>2 ],
[ 'A267623', 187, 'bignum_central_column' ],
[ 'A265427', 188, 'bignum', base=>2 ],
[ 'A267635', 189, 'bits' ],
[ 'A267636', 193, 'bits' ],
[ 'A267645', 193, 'bignum', base=>2 ],
[ 'A267646', 193, 'bignum' ],
[ 'A267673', 195, 'bits' ],
[ 'A267674', 195, 'bignum', base=>2 ],
[ 'A267675', 195, 'bignum' ],
[ 'A267676', 197, 'bits' ],
[ 'A267677', 197, 'bignum', base=>2 ],
[ 'A267678', 197, 'bignum' ],
[ 'A267687', 199, 'bits' ],
[ 'A267688', 199, 'bignum', base=>2 ],
[ 'A267689', 199, 'bignum' ],
[ 'A267679', 201, 'bits' ],
[ 'A267680', 201, 'bignum', base=>2 ],
[ 'A267681', 201, 'bignum' ],
[ 'A267683', 203, 'bits' ],
[ 'A267684', 203, 'bignum', base=>2 ],
[ 'A267685', 203, 'bignum' ],
[ 'A267704', 205, 'bits' ],
[ 'A267705', 205, 'bignum', base=>2 ],
[ 'A267708', 206, 'bits' ],
[ 'A267773', 207, 'bits' ],
[ 'A267774', 207, 'bignum' ],
[ 'A267775', 207, 'bignum', base=>2 ],
[ 'A267776', 209, 'bits' ],
[ 'A267777', 209, 'bignum', base=>2 ],
[ 'A267778', 211, 'bits' ],
[ 'A267779', 211, 'bignum', base=>2 ],
[ 'A267780', 211, 'bignum' ],
[ 'A267800', 213, 'bits' ],
[ 'A267801', 213, 'bignum', base=>2 ],
[ 'A267802', 213, 'bignum' ],
[ 'A267804', 214, 'bignum', base=>2 ],
[ 'A267805', 214, 'bignum' ],
[ 'A267810', 217, 'bits' ],
[ 'A267811', 217, 'bignum', base=>2 ],
[ 'A267812', 217, 'bignum' ],
[ 'A267813', 219, 'bits' ],
[ 'A267814', 221, 'bits' ],
[ 'A267815', 221, 'bignum', base=>2 ],
[ 'A267816', 221, 'bignum' ],
[ 'A267841', 225, 'bits' ],
[ 'A267842', 225, 'bignum', base=>2 ],
[ 'A267843', 225, 'bignum' ],
[ 'A267845', 227, 'bits' ],
[ 'A267846', 227, 'bignum', base=>2 ],
[ 'A267847', 227, 'bignum' ],
[ 'A267848', 229, 'bits' ],
[ 'A267850', 229, 'bignum', base=>2 ],
[ 'A267851', 229, 'bignum' ],
[ 'A267853', 230, 'bits' ],
[ 'A267854', 230, 'bignum', base=>2 ],
[ 'A267855', 230, 'bignum' ],
[ 'A267866', 231, 'bits' ],
[ 'A267867', 231, 'bignum', base=>2 ],
[ 'A267868', 233, 'bits' ],
[ 'A267869', 235, 'bits' ],
[ 'A267870', 237, 'bits' ],
[ 'A267871', 239, 'bits' ],
[ 'A267876', 233, 'bignum', base=>2 ],
[ 'A267877', 233, 'bignum' ],
[ 'A267878', 233, 'bits', part => 'centre' ],
[ 'A267879', 233, 'bignum_central_column' ],
[ 'A267885', 235, 'bignum', base=>2 ],
[ 'A267886', 235, 'bignum' ],
[ 'A267887', 237, 'bignum', base=>2 ],
[ 'A267888', 237, 'bignum' ],
[ 'A267889', 239, 'bignum', base=>2 ],
[ 'A267890', 239, 'bignum' ],
[ 'A267919', 243, 'bits' ],
[ 'A267920', 243, 'bignum', base=>2 ],
[ 'A267921', 243, 'bignum' ],
[ 'A267922', 245, 'bits' ],
[ 'A267923', 245, 'bignum', base=>2 ],
[ 'A267924', 245, 'bignum' ],
[ 'A267925', 246, 'bignum', base=>2 ],
[ 'A267926', 246, 'bignum' ],
[ 'A267927', 249, 'bits' ],
[ 'A267934', 249, 'bignum', base=>2 ],
[ 'A267935', 249, 'bignum' ],
[ 'A267936', 251, 'bits' ],
[ 'A267937', 251, 'bignum', base=>2 ],
[ 'A267938', 251, 'bignum' ],
[ 'A267940', 253, 'bignum', base=>2 ],
[ 'A267941', 253, 'bignum' ],
[ 'A265122', 73, 'bignum', base=>2 ],
[ 'A265156', 73, 'bignum' ],
[ 'A263428', 3, 'bits' ],
[ 'A262448', 73, 'bits' ],
[ 'A259661', 54, 'bignum_central_column' ],
[ 'A260552', 17, 'bits' ],
[ 'A260692', 17, 'bignum', base=>2 ],
[ 'A261299', 30, 'bignum_central_column' ],
[ 'A098608', 2, 'bignum', base=>2 ], # 100^n
[ 'A011557', 4, 'bignum', base=>2 ], # 10^n
[ 'A245549', 30, 'bignum', base=>2 ],
[ 'A094028', 50, 'bignum', base=>2 ],
[ 'A006943', 60, 'bignum', base=>2 ], # Sierpinski
[ 'A245548', 150, 'bignum', base=>2 ],
[ 'A100706', 151, 'bignum', base=>2 ],
[ 'A109241', 206, 'bignum', base=>2 ],
[ 'A000042', 220, 'bignum', base=>2 ], # half-width 1s
# http://oeis.org/A118110
# http://oeis.org/A245548
# characteristic func of pronics m*(m+1)
# rule=4,12,36,44,68,76,100,108,132,140,164,172,196,204,228,236
[ 'A005369', 4, 'bits' ],
[ 'A071022', 198, 'bits', part=>'left' ],
[ 'A071023', 78, 'bits', part=>'left' ],
[ 'A071024', 92, 'bits', part=>'right' ],
[ 'A071025', 124, 'bits', part=>'right' ],
[ 'A071026', 188, 'bits', part=>'right' ],
[ 'A071027', 230, 'bits', part=>'left' ],
[ 'A071028', 50, 'bits' ],
[ 'A071029', 22, 'bits' ],
[ 'A071030', 54, 'bits' ],
[ 'A071031', 62, 'bits' ],
[ 'A071032', 86, 'bits' ],
[ 'A071033', 94, 'bignum', base=>2 ],
[ 'A071034', 118, 'bits' ],
[ 'A071036', 150, 'bits' ], # same as A118110
[ 'A071037', 158, 'bits' ],
[ 'A071038', 182, 'bits' ],
[ 'A071039', 190, 'bits' ],
[ 'A071040', 214, 'bits' ],
[ 'A071041', 246, 'bits' ],
# [ 'A060576', 255, 'bits' ], # homeomorphically irreducibles ...
[ 'A070909', 28, 'bits', part=>'right' ],
[ 'A070909', 156, 'bits', part=>'right' ],
[ 'A075437', 110, 'bits' ],
[ 'A118101', 94, 'bignum' ],
[ 'A118102', 94, 'bits' ],
[ 'A118108', 54, 'bignum' ],
[ 'A118109', 54, 'bignum', base=>2 ],
[ 'A118110', 150, 'bignum', base=>2 ],
[ 'A118111', 190, 'bits' ],
[ 'A118171', 158, 'bignum' ],
[ 'A118172', 158, 'bits' ],
[ 'A118173', 188, 'bignum' ],
[ 'A118174', 188, 'bits' ],
[ 'A118175', 220, 'bits' ],
[ 'A118175', 252, 'bits' ],
[ 'A070887', 110, 'bits', part=>'left' ],
[ 'A071042', 90, 'number_of', value=>0 ],
[ 'A071043', 22, 'number_of', value=>0 ],
[ 'A071044', 22, 'number_of', value=>1 ],
[ 'A071045', 54, 'number_of', value=>0 ],
[ 'A071046', 62, 'number_of', value=>0 ],
[ 'A071047', 62, 'number_of', value=>1 ],
[ 'A071049', 110, 'number_of', value=>1, initial=>[0] ],
[ 'A071048', 110, 'number_of', value=>0, part=>'left' ],
[ 'A071050', 126, 'number_of', value=>0 ],
[ 'A071051', 126, 'number_of', value=>1 ],
[ 'A071052', 150, 'number_of', value=>0 ],
[ 'A071053', 150, 'number_of', value=>1 ],
[ 'A071054', 158, 'number_of', value=>1 ],
[ 'A071055', 182, 'number_of', value=>0 ],
[ 'A038184', 150, 'bignum' ],
[ 'A038185', 150, 'bignum', part=>'left' ], # cut after central column
[ 'A001045', 28, 'bignum', initial=>[0,1] ], # Jacobsthal
[ 'A110240', 30, 'bignum' ], # cf A074890 some strange form
[ 'A117998', 102, 'bignum' ],
[ 'A117999', 110, 'bignum' ],
[ 'A037576', 190, 'bignum' ],
[ 'A002450', 250, 'bignum', initial=>[0] ], # (4^n-1)/3 10101 extra 0 at start
[ 'A006977', 230, 'bignum', part=>'left' ],
[ 'A078176', 225, 'bignum', part=>'whole', ystart=>1, inverse=>1 ],
[ 'A051023', 30, 'bits', part=>'centre' ],
[ 'A070950', 30, 'bits' ],
[ 'A070951', 30, 'number_of', value=>0 ],
[ 'A070952', 30, 'number_of', value=>1, max_count=>400, initial=>[0] ],
[ 'A151929', 30, 'number_of_1s_first_diff', max_count=>200,
initial=>[0], # without diffs yet applied ...
],
[ 'A092539', 30, 'bignum_central_column' ],
[ 'A094603', 30, 'trailing_number_of', value=>1 ],
[ 'A094604', 30, 'new_maximum_trailing_number_of', 1 ],
[ 'A001316', 90, 'number_of', value=>1 ], # Gould's sequence
#--------------------------------------------------------------------------
# Sierpinski triangle, 8 of whole
# rule=60 right half
[ 'A047999', 60, 'bits', part=>'right' ], # Sierpinski triangle in right
[ 'A001317', 60, 'bignum' ], # Sierpinski triangle right half
[ 'A075438', 60, 'bits' ], # including 0s in left half
# rule=102 left half
[ 'A047999', 102, 'bits', part=>'left' ],
[ 'A075439', 102, 'bits' ],
[ 'A038183', 18, 'bignum' ], # Sierpinski bignums
[ 'A038183', 26, 'bignum' ],
[ 'A038183', 82, 'bignum' ],
[ 'A038183', 90, 'bignum' ],
[ 'A038183', 146, 'bignum' ],
[ 'A038183', 154, 'bignum' ],
[ 'A038183', 210, 'bignum' ],
[ 'A038183', 218, 'bignum' ],
[ 'A070886', 18, 'bits' ], # Sierpinski 0/1
[ 'A070886', 26, 'bits' ],
[ 'A070886', 82, 'bits' ],
[ 'A070886', 90, 'bits' ],
[ 'A070886', 146, 'bits' ],
[ 'A070886', 154, 'bits' ],
[ 'A070886', 210, 'bits' ],
[ 'A070886', 218, 'bits' ],
#--------------------------------------------------------------------------
# simple stuff
# whole solid, values 2^(2n)-1
[ 'A083420', 151, 'bignum' ], # 8 of
[ 'A083420', 159, 'bignum' ],
[ 'A083420', 183, 'bignum' ],
[ 'A083420', 191, 'bignum' ],
[ 'A083420', 215, 'bignum' ],
[ 'A083420', 223, 'bignum' ],
[ 'A083420', 247, 'bignum' ],
[ 'A083420', 254, 'bignum' ],
# and also
[ 'A083420', 222, 'bignum' ], # 2 of
[ 'A083420', 255, 'bignum' ],
# right half solid 2^n-1
[ 'A000225', 220, 'bignum', initial=>[0] ], # 2^n-1 want start from 1
[ 'A000225', 252, 'bignum', initial=>[0] ],
# left half solid, # 2^n-1
[ 'A000225', 206, 'bignum', part=>'left', initial=>[0] ], # 0xCE
[ 'A000225', 238, 'bignum', part=>'left', initial=>[0] ], # 0xEE
# central column only, values all 1s
[ 'A000012', 4, 'bignum', part=>'left' ],
[ 'A000012', 12, 'bignum', part=>'left' ],
[ 'A000012', 36, 'bignum', part=>'left' ],
[ 'A000012', 44, 'bignum', part=>'left' ],
[ 'A000012', 68, 'bignum', part=>'left' ],
[ 'A000012', 76, 'bignum', part=>'left' ],
[ 'A000012', 100, 'bignum', part=>'left' ],
[ 'A000012', 108, 'bignum', part=>'left' ],
[ 'A000012', 132, 'bignum', part=>'left' ],
[ 'A000012', 140, 'bignum', part=>'left' ],
[ 'A000012', 164, 'bignum', part=>'left' ],
[ 'A000012', 172, 'bignum', part=>'left' ],
[ 'A000012', 196, 'bignum', part=>'left' ],
[ 'A000012', 204, 'bignum', part=>'left' ],
[ 'A000012', 228, 'bignum', part=>'left' ],
[ 'A000012', 236, 'bignum', part=>'left' ],
#
# central column only, central values N=1,2,3,etc all integers
[ 'A000027', 4, 'central_column_N' ],
[ 'A000027', 12, 'central_column_N' ],
[ 'A000027', 36, 'central_column_N' ],
[ 'A000027', 44, 'central_column_N' ],
[ 'A000027', 76, 'central_column_N' ],
[ 'A000027', 108, 'central_column_N' ],
[ 'A000027', 132, 'central_column_N' ],
[ 'A000027', 140, 'central_column_N' ],
[ 'A000027', 164, 'central_column_N' ],
[ 'A000027', 172, 'central_column_N' ],
[ 'A000027', 196, 'central_column_N' ],
[ 'A000027', 204, 'central_column_N' ],
[ 'A000027', 228, 'central_column_N' ],
[ 'A000027', 236, 'central_column_N' ],
#
# central column only, values 2^k
[ 'A000079', 4, 'bignum' ],
[ 'A000079', 12, 'bignum' ],
[ 'A000079', 36, 'bignum' ],
[ 'A000079', 44, 'bignum' ],
[ 'A000079', 68, 'bignum' ],
[ 'A000079', 76, 'bignum' ],
[ 'A000079', 100, 'bignum' ],
[ 'A000079', 108, 'bignum' ],
[ 'A000079', 132, 'bignum' ],
[ 'A000079', 140, 'bignum' ],
[ 'A000079', 164, 'bignum' ],
[ 'A000079', 172, 'bignum' ],
[ 'A000079', 196, 'bignum' ],
[ 'A000079', 204, 'bignum' ],
[ 'A000079', 228, 'bignum' ],
[ 'A000079', 236, 'bignum' ],
# right diagonal only, values all 1, 16 of
[ 'A000012', 0x10, 'bignum' ],
[ 'A000012', 0x18, 'bignum' ],
[ 'A000012', 0x30, 'bignum' ],
[ 'A000012', 0x38, 'bignum' ],
[ 'A000012', 0x50, 'bignum' ],
[ 'A000012', 0x58, 'bignum' ],
[ 'A000012', 0x70, 'bignum' ],
[ 'A000012', 0x78, 'bignum' ],
[ 'A000012', 0x90, 'bignum' ],
[ 'A000012', 0x98, 'bignum' ],
[ 'A000012', 0xB0, 'bignum' ],
[ 'A000012', 0xB8, 'bignum' ],
[ 'A000012', 0xD0, 'bignum' ],
[ 'A000012', 0xD8, 'bignum' ],
[ 'A000012', 0xF0, 'bignum' ],
[ 'A000012', 0xF8, 'bignum' ],
# left diagonal only, values 2^k
[ 'A000079', 0x02, 'bignum', part=>'left' ],
[ 'A000079', 0x0A, 'bignum', part=>'left' ],
[ 'A000079', 0x22, 'bignum', part=>'left' ],
[ 'A000079', 0x2A, 'bignum', part=>'left' ],
[ 'A000079', 0x42, 'bignum', part=>'left' ],
[ 'A000079', 0x4A, 'bignum', part=>'left' ],
[ 'A000079', 0x62, 'bignum', part=>'left' ],
[ 'A000079', 0x6A, 'bignum', part=>'left' ],
[ 'A000079', 0x82, 'bignum', part=>'left' ],
[ 'A000079', 0x8A, 'bignum', part=>'left' ],
[ 'A000079', 0xA2, 'bignum', part=>'left' ],
[ 'A000079', 0xAA, 'bignum', part=>'left' ],
[ 'A000079', 0xC2, 'bignum', part=>'left' ],
[ 'A000079', 0xCA, 'bignum', part=>'left' ],
[ 'A000079', 0xE2, 'bignum', part=>'left' ],
[ 'A000079', 0xEA, 'bignum', part=>'left' ],
# bits, characteristic of square
[ 'A010052', 0x02, 'bits' ],
[ 'A010052', 0x0A, 'bits' ],
[ 'A010052', 0x22, 'bits' ],
[ 'A010052', 0x2A, 'bits' ],
[ 'A010052', 0x42, 'bits' ],
[ 'A010052', 0x4A, 'bits' ],
[ 'A010052', 0x62, 'bits' ],
[ 'A010052', 0x6A, 'bits' ],
[ 'A010052', 0x82, 'bits' ],
[ 'A010052', 0x8A, 'bits' ],
[ 'A010052', 0xA2, 'bits' ],
[ 'A010052', 0xAA, 'bits' ],
[ 'A010052', 0xC2, 'bits' ],
[ 'A010052', 0xCA, 'bits' ],
[ 'A010052', 0xE2, 'bits' ],
[ 'A010052', 0xEA, 'bits' ],
);
# {
# require Data::Dumper;
# foreach my $i (0 .. $#data) {
# my $e1 = $data[$i];
# my @a1 = @$e1; shift @a1;
# my $a1 = Data::Dumper->Dump([\@a1],['args']);
# ### $e1
# ### @a1
# ### $a1
# foreach my $j ($i+1 .. $#data) {
# my $e2 = $data[$j];
# my @a2 = @$e2; shift @a2;
# my $a2 = Data::Dumper->Dump([\@a2],['args']);
#
# if ($a1 eq $a2) {
# print "duplicate $e1->[0] = $e2->[0] params $a1\n";
# }
# }
# }
# }
foreach my $elem (@data) {
### $elem
my ($anum, $rule, $method, @params) = @$elem;
my $func = main->can($method) || die "Unrecognised method $method";
&$func ($anum, $rule, @params);
}
#------------------------------------------------------------------------------
# number of 0s or 1s in row
sub number_of {
my ($anum, $rule, %params) = @_;
my $part = $params{'part'} || 'whole';
my $want_value = $params{'value'} // 1;
my $max_count = $params{'max_count'} || 100;
MyOEIS::compare_values
(anum => $anum,
name => "$anum number of ${want_value}s in rows rule $rule, $part",
max_count => $max_count,
func => sub {
my ($count) = @_;
return number_of_make_values($count, $anum, $rule, %params);
});
}
sub number_of_1s_first_diff {
my ($anum, $rule, %params) = @_;
my $max_count = $params{'max_count'};
MyOEIS::compare_values
(anum => $anum,
name => "$anum number of 1s first differences",
max_count => $max_count,
func => sub {
my ($count) = @_;
my $aref = number_of_make_values($count+1, $anum, $rule, %params);
return [ MyOEIS::first_differences(@$aref) ];
});
}
sub number_of_make_values {
my ($count, $anum, $rule, %params) = @_;
my $initial = $params{'initial'} || [];
my $part = $params{'part'} || 'whole';
my $want_value = $params{'value'} // 1;
my $max_count = $params{'max_count'};
my $path = Math::PlanePath::CellularRule->new (rule => $rule);
my @got = @$initial;
for (my $y = 0; @got < $count; $y++) {
my $number_of = 0;
foreach my $x (($part eq 'right' || $part eq 'centre' ? 0 : -$y)
.. ($part eq 'left' || $part eq 'centre' ? 0 : $y)) {
my $n = $path->xy_to_n ($x, $y);
my $got_value = (defined $n ? 1 : 0);
if ($got_value == $want_value) {
$number_of++;
}
}
push @got, $number_of;
}
return \@got;
}
#------------------------------------------------------------------------------
# number of 0s or 1s in row at the rightmost end
sub trailing_number_of {
my ($anum, $rule, %params) = @_;
my $initial = $params{'initial'} || [];
my $part = $params{'part'} || 'whole';
my $want_value = $params{'value'} // 1;
MyOEIS::compare_values
(anum => $anum,
name => "$anum trailing number of ${want_value}s in rows rule $rule",
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::CellularRule->new (rule => $rule);
my @got = @$initial;
for (my $y = 0; @got < $count; $y++) {
my $number_of = 0;
for (my $x = $y; $x >= -$y; $x--) {
my $n = $path->xy_to_n ($x, $y);
my $got_value = (defined $n ? 1 : 0);
if ($got_value == $want_value) {
$number_of++;
} else {
last;
}
}
push @got, $number_of;
}
return \@got;
});
}
sub new_maximum_trailing_number_of {
my ($anum, $rule, $want_value) = @_;
my $path = Math::PlanePath::CellularRule->new (rule => $rule);
my ($bvalues, $lo, $filename) = MyOEIS::read_values($anum);
my @got;
if ($bvalues) {
MyTestHelpers::diag ("$anum new_maximum_trailing_number_of");
if ($anum eq 'A094604') {
# new max only at Y=2^k, so limit search
if ($#$bvalues > 10) {
$#$bvalues = 10;
}
}
my $prev = 0;
for (my $y = 0; @got < @$bvalues; $y++) {
my $count = 0;
for (my $x = $y; $x >= -$y; $x--) {
my $n = $path->xy_to_n ($x, $y);
my $got_value = (defined $n ? 1 : 0);
if ($got_value == $want_value) {
$count++;
} else {
last;
}
}
if ($count > $prev) {
push @got, $count;
$prev = $count;
}
}
if (! streq_array(\@got, $bvalues)) {
MyTestHelpers::diag ("bvalues: ",join(',',@{$bvalues}[0..20]));
MyTestHelpers::diag ("got: ",join(',',@got[0..20]));
}
}
skip (! $bvalues,
streq_array(\@got, $bvalues),
1, "$anum");
}
#------------------------------------------------------------------------------
# bignum rows
sub bignum {
my ($anum, $rule, %params) = @_;
my $part = $params{'part'} || 'whole';
my $initial = $params{'initial'} || [];
my $ystart = $params{'ystart'} || 0;
my $inverse = $params{'inverse'} ? 1 : 0; # for bitwise invert
my $base = $params{'base'} || 10;
my $max_count = $params{'max_count'};
# if ($anum eq 'A000012') { # trim all-ones
# if ($#$bvalues > 50) { $#$bvalues = 50; }
# }
MyOEIS::compare_values
(anum => $anum,
name => "$anum bignums $part, inverse=$inverse",
max_count => $max_count,
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::CellularRule->new (rule => $rule);
my @got = @$initial;
require Math::BigInt;
for (my $y = $ystart; @got < $count; $y++) {
my $b = Math::BigInt->new(0);
foreach my $x (($part eq 'right' ? 0 : -$y)
.. ($part eq 'left' ? 0 : $y)) {
my $bit = ($path->xy_is_visited($x,$y) ? 1 : 0);
if ($inverse) { $bit ^= 1; }
$b = 2*$b + $bit;
}
if ($base == 2) {
$b = $b->as_bin;
$b =~ s/^0b//;
}
push @got, "$b";
}
return \@got;
});
}
#------------------------------------------------------------------------------
# 0/1 by rows
sub bits {
my ($anum, $rule, %params) = @_;
### bits(): @_
my $part = $params{'part'} || 'whole';
my $initial = $params{'initial'} || [];
MyOEIS::compare_values
(anum => $anum,
name => "$anum 0/1 rows rule $rule, $part",
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::CellularRule->new (rule => $rule);
my @got = @$initial;
OUTER: for (my $y = 0; ; $y++) {
foreach my $x (($part eq 'right' || $part eq 'centre' ? 0 : -$y)
.. ($part eq 'left' || $part eq 'centre' ? 0 : $y)) {
last OUTER if @got >= $count;
push @got, ($path->xy_to_n ($x, $y) ? 1 : 0);
}
}
return \@got;
});
}
#------------------------------------------------------------------------------
# bignum central vertical column in decimal
sub bignum_central_column {
my ($anum, $rule, %params) = @_;
my $base = $params{'base'} || 10;
MyOEIS::compare_values
(anum => $anum,
name => "$anum central column bignum, decimal",
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::CellularRule->new (rule => $rule);
my @got;
require Math::BigInt;
my $b = Math::BigInt->new(0);
for (my $y = 0; @got < $count; $y++) {
my $bit = ($path->xy_to_n (0, $y) ? 1 : 0);
$b = $base*$b + $bit;
push @got, "$b";
}
return \@got;
});
}
#------------------------------------------------------------------------------
# N values of central vertical column
sub central_column_N {
my ($anum, $rule) = @_;
MyOEIS::compare_values
(anum => $anum,
name => "$anum central column N",
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::CellularRule->new (rule => $rule);
my @got;
for (my $y = 0; @got < $count; $y++) {
push @got, $path->xy_to_n (0, $y);
}
return \@got;
});
}
#------------------------------------------------------------------------------
# A071029 rule 22 ... ?
#
# 22 = 00010110
# 111 -> 0
# 110 -> 0
# 101 -> 0
# 100 -> 1
# 011 -> 0
# 010 -> 1
# 001 -> 1
# 000 -> 0
# 0,
# 1, 0, 1,
# 0, 1, 0, 1, 0,
# 1, 0, 1, 0, 1, 0, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0,
# 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
# 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
# 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0,
# 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0
# 0,
# 1,
# 0, 1, 0,
# 1, 0, 1, 0, 1,
# 0, 1, 0, 1, 0, 1, 0,
# 1, 0, 1, 0, 1, 0, 1, 0, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
# 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0, 1,
# 0
# A071043 Number of 0's in n-th row of triangle in A071029.
# 0, 0, 3, 1, 7, 5, 9, 3, 15, 13, 17, 11, 21, 15, 21, 7, 31, 29, 33, 27,
# 37, 31, 37, 23, 45, 39, 45, 31, 49, 35, 45, 15, 63, 61, 65, 59, 69, 63,
# 69, 55, 77, 71, 77, 63, 81, 67, 77, 47, 93, 87, 93, 79, 97, 83, 93, 63,
# 105, 91, 101, 71, 105, 75, 93, 31, 127, 125, 129
#
# A071044 Number of 1's in n-th row of triangle in A071029.
# 1, 3, 2, 6, 2, 6, 4, 12, 2, 6, 4, 12, 4, 12, 8, 24, 2, 6, 4, 12, 4, 12,
# 8, 24, 4, 12, 8, 24, 8, 24, 16, 48, 2, 6, 4, 12, 4, 12, 8, 24, 4, 12,
# 8, 24, 8, 24, 16, 48, 4, 12, 8, 24, 8, 24, 16, 48, 8, 24, 16, 48, 16,
# 48, 32, 96, 2, 6, 4, 12, 4, 12, 8, 24, 4, 12, 8, 24, 8, 24, 16, 48
#
# *** *** *** ***
# * * * *
# *** ***
# * *
# *** ***
# * *
# ***
# *
#------------------------------------------------------------------------------
# A071026 rule 188
# rows n+1
#
# 1,
# 1, 0,
# 0, 1, 1,
# 0, 1, 0, 1,
# 1, 1, 1, 1, 0,
# 0, 0, 1, 1, 0, 1,
# 1, 1, 1, 1, 1, 1, 1,
# 1, 0, 1, 1, 0, 0, 1, 1,
# 1, 1, 0, 0, 0, 0, 0, 0, 1,
# 1, 1, 1, 1, 1, 1, 0, 1, 0, 0,
# 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1,
# 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0,
# 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0,
# 0, 1, 1, 1, 0, 1, 1, 0
#
# * *** *
# ** ***
# *** *
# ****
# * *
# **
# *
#------------------------------------------------------------------------------
# A071023 rule 78
# *** * * *
# ** * * *
# *** * *
# ** * *
# *** *
# ** *
# ***
# **
# *
# 1, 1, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
# 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
# 1, 1, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
# 1, 1, 1, 1, 1, 1, 1, 1, 1,
# 0, 1, 1, 1, 1,
# 0, 1, 1, 1,
# 0, 1, 0,
# 1, 1, 1
# 111 ->
# 110 ->
# 101 ->
# 100 ->
# 011 ->
# 010 -> 1
# 001 -> 1
# 000 ->
# 1,
# 1, 1,
# 0, 1, 0,
# 1, 0, 1, 0,
# 1, 0, 1, 0, 1,
# 0, 1, 0, 1, 0, 1,
# 0, 1, 0, 1, 1, 0, 1,
# 0, 1, 0, 1, 0, 1, 0, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0,
# 1, 0, 1, 0, 1, 1, 1, 0, 1, 0,
# 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1,
# 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1,
# 1, 1, 0, 1, 0, 1, 1, 1
#------------------------------------------------------------------------------
# A071024 rule 92
# 0, 1, 0, 1, 0,
# 1, 1, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
# 1, 1, 1, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
# 1, 1, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
# 1, 1, 1, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0
#------------------------------------------------------------------------------
# A071027 rule 230
# * *** *** *
# *** *** **
# * *** ***
# *** ****
# * *** *
# *** **
# * ***
# ****
# * *
# **
# *
# 1, 1, 1, 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 1, 1, 0,
# 1
#------------------------------------------------------------------------------
# # A071035 rule 126 sierpinski
#
# 1,
# 1, 0, 1,
# 1, 0, 1,
# 1, 0, 0, 0, 1,
# 1, 1, 1, 0, 1, 0, 1, 1, 1,
# 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1,
# 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0,
# 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1,
# 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0
#------------------------------------------------------------------------------
# A071022 rule 70,198
# ** * * * *
# * * * * *
# ** * * *
# * * * *
# ** * *
# * * *
# ** *
# * *
# **
# *
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 1, 1, 1, 1, 1, 0,
# 1, 1, 1, 0,
# 1, 1, 0,
# 1, 0,
# 1, 1, 1, 0,
# 1, 0,
# 1, 1, 0,
# 1, 0,
# 1, 0,
# 1, 1, 1, 0,
# 1, 0,
# 1, 0,
# 1, 1, 0,
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 1, 1, 0,
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 1, 0,
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 0,
# 1, 1, 1, 0,
# 1, 0,
# 1, 0
#------------------------------------------------------------------------------
# A071030 - rule 54, rows 2n+1
# 0,
# 1, 0, 1,
# 0, 1, 0, 1, 0,
# 1, 0, 1, 0, 1, 0, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0,
# 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1,
# 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
# 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0,
# 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1,
# 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0
#------------------------------------------------------------------------------
# A071039 rule 190, rows 2n+1
# 1,
# 0, 1, 0,
# 1, 1, 1, 1, 1,
# 0, 1, 0, 1, 0, 1, 0,
# 1, 0, 1, 0, 1, 0, 1, 1, 1,
# 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
# 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
# 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
# 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1
#------------------------------------------------------------------------------
# A071036 rule 150
# ** ** *** ** **
# * * * * *
# *** *** ***
# * * *
# ** * **
# * * *
# ***
# *
# 1,
# 0, 1, 1,
# 0, 1, 1, 0, 0,
# 0, 1, 1, 1, 1, 0, 1,
# 0, 1, 1, 0, 0, 0, 1, 1, 1,
# 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1,
# 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1,
# 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1,
# 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1,
# 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1
#------------------------------------------------------------------------------
# A071022 rule 70,198
# A071023 rule 78
# A071024 rule 92
# A071025 rule 124
# A071026 rule 188
# A071027 rule 230
# A071028 rule 50 ok
# A071029 rule 22
# A071030 rule 54 -- cf A118108 bignum A118109 binary bignum
# A071031 rule 62
# A071032 rule 86
# A071033 rule 94
# A071034 rule 118
# A071035 rule 126 sierpinski
# A071036 rule 150
# A071037 rule 158
# A071038 rule 182
# A071039 rule 190
# A071040 rule 214
# A071041 rule 246
#
# A071042 num 0s in A070886 rule 90 sierpinski ok
# A071043 num 0s in A071029 rule 22 ok
# A071044 num 1s in A071029 rule 22 ok
# A071045 num 0s in A071030 rule 54 ok
# A071046 num 0s in A071031 rule 62 ok
# A071047
# A071048
# A071049
# A071050
# A071051 num 1s in A071035 rule 126 sierpinski
# A071052
# A071053
# A071054
# A071055
#
exit 0;