# Copyright 2010 Kevin Ryde

# This file is part of Math-Image.
#
# Math-Image 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-Image 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-Image.  If not, see <http://www.gnu.org/licenses/>.

package App::MathImage::Values::Pentagonal;
use 5.004;
use strict;
use warnings;
use Locale::TextDomain 'App-MathImage';

use base 'App::MathImage::Values';

use vars '$VERSION';
$VERSION = 36;

use constant name => __('Pentagonal Numbers');
use constant description => __('The pentagonal numbers 1,5,12,22,etc, (3k-1)*k/2.');
use constant oeis => 'A000326';

# uncomment this to run the ### lines
#use Smart::Comments;

sub new {
  my ($class, %options) = @_;
  my $lo = $options{'lo'} || 0;
  return bless { i => 0
               }, $class;
}
sub next {
  my ($self) = @_;
  return $self->ith($self->{'i'}++);
}
sub ith {
  my ($class_or_self, $i) = @_;
  return (3*$i-1)*$i/2;
}

# i = 1/6 + sqrt(2/3 * $n + 1/36)
#   = 1/6 * (1 + 6*sqrt(2/3 * $n + 1/36))
#   = 1/6 * (1 + sqrt(36 * (2/3 * $n + 1/36)))
#   = 1/6 * (1 + sqrt(24*$n + 1)))
#
sub pred {
  my ($self, $n) = @_;
  return ($n <= 0
          ? ($n == 0)
          : do {
            my $sqrt = (sqrt(24*$n+1) + 1) / 6;
            (int($sqrt) == $sqrt)
          });
}


1;
__END__
