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use Algorithm::Combinatorics qw[ variations_with_repetition ];;

...

$d = 0; $_->[0]+1 == $_->[1] or $_->[1]+1 == $_->[2] and ++$d for @c; 
+print $d;;
7922

$d = 0; $_->[0] == $_->[2]+1 and ++$d for @c; print $d;;
8010