NAME

Math::NumSeq::Triangular -- triangular numbers

SYNOPSIS

use Math::NumSeq::Triangular;
my $seq = Math::NumSeq::Triangular->new;
my ($i, $value) = $seq->next;

DESCRIPTION

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.

FUNCTIONS

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

$seq = Math::NumSeq::Triangular->new ()

Create and return a new sequence object.

Random Access

$value = $seq->ith($i)

Return $i*($i+1)/2.

$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 floor.

$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)

SEE ALSO

Math::NumSeq, Math::NumSeq::Pronic, Math::NumSeq::Squares

HOME PAGE

http://user42.tuxfamily.org/math-numseq/index.html

LICENSE

Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019, 2020 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.

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/>.