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.
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 forceil
or lower forfloor
. $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/mathnumseq/index.html
LICENSE
Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019 Kevin Ryde
MathNumSeq 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.
MathNumSeq 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 MathNumSeq. If not, see <http://www.gnu.org/licenses/>.