I am sure there is a mathematical equation that would simplify this
Well, here's it. I hope it works.
Has someone written a test program that compares the outputs
of different solutions in this thread with each other?
#!perl
use warnings;
use strict;
my($n, $wd, $fmt, $x, $y, $r);
$n = int($ARGV[1]  5);
$wd = length($n**2);
$fmt = "%${wd}d ";
for $x (0 .. $n  1) {
for $y (0 .. $n  1) {
$r = $x <= $y ?
$x + $y <= $n  1 ?
4*$x**2 + 4*$n*$x  $x + $y + 1 :
4*$y**2 + 4*$n*$y  5*$y + $x + 2*$n
+ 1 :
$x + $y <= $n  1 ?
4*$y**2 + 4*$n*$y  7*$y  $x + 4*$n
+ 3 :
4*$x**2 + 4*$n*$x  3*$x  $y + 2*$n
+ 1;
printf $fmt, $r;
}
print "\n";
}
__END__
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