A072377 Number of pairs of orthogonal Latin squares of order n.

1, 0, 36, 3456, 3110400, 0, 3131834388480000, 32162058365970677760000, 19083454070548282639185346560000

Offset

1,3

Comments

This sequence counts unordered pairs. The number of ordered pairs of MOLS is exactly double this sequence.

Links

Table of n, a(n) for n=1..9.

J. Egan and I. M. Wanless, Enumeration of MOLS of small order, Mathematics of Computation 85, 2016, 799-824.

Ian Wanless, Data on MOLS

Eric Weisstein's World of Mathematics, Latin Square

Crossrefs

Equals n!n!(n-1)!/2 times A266166 (except for the degenerate case n=1). Cf. A000315, A002860, A266167, A266168, A266169, A266170, A266171, A266172, A266173.

Sequence in context: A303339 A034983 A291911 * A364175 A209267 A120349

Adjacent sequences: A072374 A072375 A072376 * A072378 A072379 A072380

Keyword

nonn,more

Author

Eric W. Weisstein, Jul 19 2002

Extensions

More terms (and corrected the degenerate first term) from Ian Wanless, Dec 22 2015

Status

approved