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examples/faulhaber_coefficients.pl  view on Meta::CPAN

#!/usr/bin/perl

# Compute the Faulhaber triangle of coffiecients.

# See also:
#   https://en.wikipedia.org/wiki/Faulhaber's_formula
#   https://en.wikipedia.org/wiki/Vandermonde_matrix

use 5.014;
use lib qw(../lib);
use experimental qw(signatures);

use Math::MatrixLUP;
use Math::AnyNum qw(:overload ipow);

sub faulhaber_coefficients ($n) {

examples/fibonacci_of_k-th_order.pl  view on Meta::CPAN

#!/usr/bin/perl

# General formula for computing the k-th order Fibonacci numbers, using exponentation by squaring.

# OEIS sequences:
#   https://oeis.org/A000045    (2-nd order: Fibonacci numbers)
#   https://oeis.org/A000073    (3-rd order: Tribonacci numbers)
#   https://oeis.org/A000078    (4-th order: Tetranacci numbers)
#   https://oeis.org/A001591    (5-th order: Pentanacci numbers)

# See also:
#   https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers
#   https://en.wikipedia.org/wiki/Exponentiation_by_squaring