# Copyright 2010, 2011 Kevin Ryde
# This file is part of Math-NumSeq.
#
# Math-NumSeq 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-NumSeq 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-NumSeq. If not, see <http://www.gnu.org/licenses/>.
package Math::NumSeq::PentagonalGeneralized;
use 5.004;
use strict;
use Math::NumSeq;
use base 'Math::NumSeq';
use vars '$VERSION';
$VERSION = 38;
# uncomment this to run the ### lines
#use Smart::Comments;
# use constant name => Math::NumSeq::__('Pentagonal Numbers, generalized');
use constant description => Math::NumSeq::__('The generalized pentagonal numbers 1, 2, 5, 7, 15, 22, 22, 26, etc, (3k-1)*k/2 for k positive and negative. This is the plain pentagonal and second pentagonals taken together.');
use constant oeis_anum => 'A001318';
sub rewind {
my ($self) = @_;
$self->{'i'} = $self->i_start;
$self->{'neg'} = 1;
}
sub next {
my ($self) = @_;
my $i = $self->{'i'}++;
# ENHANCE-ME: step by 2*i etc
return ($i, $self->ith($i));
# if ($self->{'neg'} ^= 1) {
# my $i = $self->{'i'};
# return ($i, (3*-$i+1)*-$i/2);
# } else {
# my $i = $self->{'i'}++;
# return ($i, (3*$i+1)*$i/2);
# }
}
sub ith {
my ($self, $i) = @_;
if ($i & 1) {
$i = ($i - 1) / 2;
return (3*-$i+1)*-$i/2
} else {
$i /= 2;
return (3*$i+1)*$i/2;
}
}
# sub pred {
# my ($self, $n) = @_;
# return ($n & 1);
# }
1;
__END__