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T_n == 1 (mod 3) when n == 1 (mod 3) T_n == 0 (mod 3) otherwise
if n == 0 (mod 3), require A A A or B B B if n == 1 (mod 3), require A A B if n == 2 (mod 3), require A B B
sub p_tri { my $num = shift; ... my $t = int((sqrt($x) + 1)/2); return +((2 * $t - 1) * (2 * $t - 1) == $x) ? 0 : --$t; }
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