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#! /opt/local/bin/perl
#
# leonardo_numbers.pl
#
# PWC41
# TASK #2
# Write a script to display first 20 Leonardo Numbers. Please checkout wiki page for more information.
# For example:
#
# L(0) = 1
# L(1) = 1
# L(2) = L(0) + L(1) + 1 = 3
# L(3) = L(1) + L(2) + 1 = 5
# and so on.
#
# method: because we have the growing series directly available to
# refer to no recursion is required. I have made the function
# return a list for any quantity > 0, displayed with a nice little
# header.
#
# As-is can handle up to L(90)
# L(90) = 5,760,134,388,741,632,239
#
# 2020 colin crain
## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
use warnings;
use strict;
use feature ":5.26";
## ## ## ## ## MAIN
my $quan = shift @ARGV // 20;
say "the first $quan Leonardo numbers:";
say "";
say "index | number";
say "-------+--------";
my $i;
printf "%-2d %d\n", ++$i, $_ for make_leonardo($quan)->@*;
## ## ## ## ## SUBS
sub make_leonardo {
## construct a list of the first n Leonardo numbers
## requires no recursion if we have the growing list to refer to
my $quan = shift;
my $list = [1];
push $list->@*, 1 if $quan > 1; ## now [1,1]
while ( scalar $list->@* <= $quan-1 ) {
push $list->@*, $list->[-1] + $list->[-2] + 1; ## sum last two elements + 1
}
return $list;
}
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