Math::NumSeq::Triangular -- triangular numbers
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, ...
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 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)
Math::NumSeq, Math::NumSeq::Pronic, Math::NumSeq::Squares
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/>.
To install Math::NumSeq, copy and paste the appropriate command in to your terminal.
perl -MCPAN -e shell
For more information on module installation, please visit the detailed CPAN module installation guide.