#!/usr/bin/perl

use Tie::Math qw(f X Y);

my %pascal;
tie %pascal, 'Tie::Math', sub {
                              if( X <= Y and Y > 0 and X > 0 ) {
                                  f(X,Y) = f(X-1,Y-1) + f(X,Y-1);
                             }
                             else {
                                 f(X,Y) = 0;
                             }
                         },
                         sub {
                             f(1,1) = 1;
                             f(1,2) = 1;
                             f(2,2) = 1;
                         };

#'#

my $height = 5;
for my $y (1..$height) {
    print " " x ($height - $y);
    for my $x (1..$y) {
        print $pascal{$x,$y};
        }
        print "\n";
}