Math::NumSeq::Triangular -- triangular numbers
use Math::NumSeq::Triangular; my $seq = Math::NumSeq::Triangular->new; my ($i, $value) = $seq->next;
The triangular numbers i*(i+1)/2,
0, 1, 3, 6, 10, 15, 21, 28, ... starting i=0
The numbers are how many points are in an equilateral triangle of side i,
* i=1 1 * i=2 3 * * * * * i=3 6 * * * * * * i=4 10 * * * * * * *
From a given i, the next value is formed by adding i+1, being a new row of that length on the bottom of the triangle.
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::Triangular->new ()
Create and return a new sequence object.
$value = $seq->ith($i)
$bool = $seq->pred($value)
Return true if
$value is a triangular number, ie. i*(i+1)/2 for some integer i.
$i = $seq->value_to_i_ceil($value)
$i = $seq->value_to_i_floor($value)
Return the index i of
$value, or if
$value is not a triangular number then the next higher for
ceil or lower for
$i = $seq->value_to_i_estimate($value)
Return an estimate of the i corresponding to
$value. This is value=i*(i+1)/2 is inverted to
$i = int ((sqrt(8*$value + 1) - 1)/2)
Copyright 2010, 2011, 2012, 2013 Kevin Ryde
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.
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