A point I forgot to make:

Though it's implied by the program in my previous message, it's good to stress
that the simple formula:

$m*$n+4-int(($m+2)*($n+2)/5);

works for any board where both dimensions >= 16

In particular it works for all square boards ($m == $n) with size >= 7 except 
for 13 x 13. So you only need a table with a few exceptions, the rest of the 
square boards can be directly calculated
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