#!/usr/bin/perl -w
# Copyright 2012, 2013, 2014 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/>.
use 5.004;
use strict;
use Math::PlanePath::AlternatePaper;
use Test;
plan tests => 14;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
# uncomment this to run the ### lines
#use Smart::Comments '###';
my $paper = Math::PlanePath::AlternatePaper->new;
#------------------------------------------------------------------------------
# A052955 single-visited points to N=2^k
MyOEIS::compare_values
(anum => 'A052955',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got = (1); # extra initial 1
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_n_to_singles ($paper, 2**$k);
}
return \@got;
});
# A052940 single-visited points to N=4^k
MyOEIS::compare_values
(anum => 'A052940',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got = (1); # initial 1 instead of 2
for (my $k = 1; @got < $count; $k++) {
push @got, MyOEIS::path_n_to_singles ($paper, 4**$k);
}
return \@got;
});
#------------------------------------------------------------------------------
# A122746 area increment to N=2^k
MyOEIS::compare_values
(anum => 'A122746',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 2; @got < $count; $k++) {
push @got, (MyOEIS::path_enclosed_area($paper, 2**($k+1))
- MyOEIS::path_enclosed_area($paper, 2**$k));
}
return \@got;
});
#------------------------------------------------------------------------------
# A052955 single-visit points to N=2^k
MyOEIS::compare_values
(anum => 'A052955',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got = (1);
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_n_to_singles($paper, 2**$k);
}
return \@got;
});
#------------------------------------------------------------------------------
# A028399 boundary to N=2*4^k
MyOEIS::compare_values
(anum => 'A028399',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got = (0);
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_boundary_length($paper, 2*4**$k);
}
return \@got;
});
# A131128 boundary to N=4^k
MyOEIS::compare_values
(anum => 'A131128',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got = (1);
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_boundary_length($paper, 4**$k);
}
return \@got;
});
# A027383 boundary/2 to N=2^k
# is also boundary length verticals or horizontals since boundary is half
# verticals and half horizontals
MyOEIS::compare_values
(anum => 'A027383',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_boundary_length($paper, 2**$k) / 2;
}
return \@got;
});
#------------------------------------------------------------------------------
# A060867 area to N=2*4^k
MyOEIS::compare_values
(anum => 'A060867',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 1; @got < $count; $k++) {
push @got, MyOEIS::path_enclosed_area($paper, 2*4**$k);
}
return \@got;
});
# A134057 area to N=4^k
MyOEIS::compare_values
(anum => 'A134057',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_enclosed_area($paper, 4**$k);
}
return \@got;
});
# A027556 area*2 to N=2^k
MyOEIS::compare_values
(anum => 'A027556',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_enclosed_area($paper, 2**$k) * 2;
}
return \@got;
});
#------------------------------------------------------------------------------
# A106665 -- turn 1=left, 0=right
# OFFSET=0 cf first turn at N=1 here
MyOEIS::compare_values
(anum => 'A106665',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'AlternatePaper',
turn_type => 'Left');
my @got;
while (@got < $count) {
my ($i,$value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A090678 "non-squashing partitions" A088567 mod 2
# and A121241 which is 1,-1
# almost but not quite arms=2 turn_type=Left
# A121241 1,-1
# A110036 2,0,-2
# A110037 1,0,-1
# MyOEIS::compare_values
# (anum => 'A090678',
# func => sub {
# my ($count) = @_;
# require Math::NumSeq::PlanePathTurn;
# my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'AlternatePaper,arms=2',
# turn_type => 'Left');
# my @got = (1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0,1);
# while (@got < $count) {
# my ($i,$value) = $seq->next;
# push @got, $value;
# }
# return \@got;
# });
#------------------------------------------------------------------------------
# A209615 Completely multiplicative with a(p^e) = 1 if p == 1 (mod 4),
# a(p^e) = (-1)^e otherwise.
MyOEIS::compare_values
(anum => 'A209615',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $paper,
turn_type => 'LSR');
my @got;
while (@got < $count) {
my ($i,$value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A020985 - Golay/Rudin/Shapiro is dX and dY alternately
# also is dSum in Math::NumSeq::PlanePathDelta
MyOEIS::compare_values
(anum => q{A020985},
func => sub {
my ($count) = @_;
my @got;
for (my $n = $paper->n_start; @got < $count; ) {
{
my ($dx, $dy) = $paper->n_to_dxdy ($n++);
push @got, $dx;
}
last unless @got < $count;
{
my ($dx, $dy) = $paper->n_to_dxdy ($n++);
push @got, $dy;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A020991 - position of last occurance of n, last time of X+Y=n
MyOEIS::compare_values
(anum => 'A020991',
func => sub {
my ($count) = @_;
my @got;
my @occur;
my $target = 1;
for (my $n = $paper->n_start + 1; @got < $count; $n++) {
my ($x, $y) = $paper->n_to_xy ($n);
my $d = $x + $y;
$occur[$d]++;
if ($occur[$d] == $d) {
push @got, $n-1;
$target++;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A093573+1 - triangle of positions where cumulative=k
# cumulative A020986 starts n=0 for GRS(0)=0 (A020985)
# 0,
# 1, 3,
# 2, 4, 6,
# 5, 7, 13, 15,
# 8, 12, 14, 16, 26,
# 9, 11, 17, 19, 25, 27
#
# cf diagonals
# 0
# 1
# 2, 4
# 3,7, 5
# 8, 6,14, 16
# 9,13, 15,27, 17
MyOEIS::compare_values
(anum => 'A093573',
func => sub {
my ($count) = @_;
my @got;
OUTER: for (my $sum = 1; ; $sum++) {
my @n_list;
foreach my $y (0 .. $sum) {
my $x = $sum - $y;
push @n_list, $paper->xy_to_n_list($x,$y);;
}
@n_list = sort {$a<=>$b} @n_list;
foreach my $n (@n_list) {
last OUTER if @got >= $count;
push @got, $n-1;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A020986 - GRS cumulative
# X+Y, starting from N=1 (doesn't have X+Y=0 for N=0)
MyOEIS::compare_values
(anum => 'A020986',
func => sub {
my ($count) = @_;
my @got;
for (my $n = $paper->n_start + 1; @got < $count; $n++) {
my ($x, $y) = $paper->n_to_xy ($n);
push @got, $x+$y;
}
return \@got;
});
# is X coord undoubled, starting from N=2 (doesn't have X=0 for N=0)
MyOEIS::compare_values
(anum => q{A020986},
func => sub {
my ($count) = @_;
my @got;
for (my $n = 2; @got < $count; $n += 2) {
my ($x, $y) = $paper->n_to_xy ($n);
push @got, $x;
}
return \@got;
});
#------------------------------------------------------------------------------
# A022155 - positions of -1, is S,W steps
MyOEIS::compare_values
(anum => 'A022155',
func => sub {
my ($count) = @_;
my @got;
for (my $n = $paper->n_start; @got < $count; $n++) {
my ($dx,$dy) = $paper->n_to_dxdy($n);
if ($dx < 0 || $dy < 0) {
push @got, $n;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A203463 - positions of 1, is N,E steps
MyOEIS::compare_values
(anum => 'A203463',
func => sub {
my ($count) = @_;
my @got;
for (my $n = $paper->n_start; @got < $count; $n++) {
my ($dx,$dy) = $paper->n_to_dxdy($n);
if ($dx > 0 || $dy > 0) {
push @got, $n;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A020990 - Golay/Rudin/Shapiro * (-1)^k cumulative, is Y coord undoubled,
# except N=0
MyOEIS::compare_values
(anum => 'A020990',
func => sub {
my ($count) = @_;
my @got;
for (my $n = 2; @got < $count; $n += 2) {
my ($x, $y) = $paper->n_to_xy ($n);
push @got, $y;
}
return \@got;
});
MyOEIS::compare_values
(anum => q{A020990},
func => sub {
my ($count) = @_;
my @got;
for (my $n = $paper->n_start + 1; @got < $count; $n++) {
my ($x, $y) = $paper->n_to_xy ($n);
push @got, $x-$y;
}
return \@got;
});
#------------------------------------------------------------------------------
# A212591 - position of first occurance of n, first time getting to X+Y=n
# seq 0, 1, 2, 5, 8, 9, 10, 21, 32, 33, 34, 37, 40, 41, 42, 85
# N 0 1 2 3 6, 9, 10, 11, 22, ...
MyOEIS::compare_values
(anum => 'A212591',
max_count => 1000, # because simple linear search
func => sub {
my ($count) = @_;
my @got;
my $target = 1;
for (my $n = $paper->n_start + 1; @got < $count; $n++) {
my ($x, $y) = $paper->n_to_xy ($n);
my $d = $x + $y;
if ($d == $target) {
push @got, $n-1;
$target++;
}
}
return \@got;
});
#------------------------------------------------------------------------------
exit 0;