of the pseudo-anti-symmetric type (sum of anti-symmetric and diagonal). A072148. (cfr Aug 2003). Just submitted result for n=6. The periods still are divisors of 12. Weird. Realised that block matrices along the diagonal are cheap and predictable. So I did a count without'm, and eleminated sign change, transposes and mirroring over the anti-diagonal too. Got 1, 3, 12, 107, 951, 10923... (under submission). Funny property: only the even n give some matrices with all-zero diagonals, the odd n don't. But why period k | 12 ? Wouter.