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

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

Offset: 1

Author

Eric W. Weisstein, Jul 19 2002

Keywords

• nonn
• more

Comments

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

Links

• 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.

Extensions

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