A098679 Total number of Latin cubes of order n.

1, 2, 24, 55296, 2781803520, 994393803303936000

Offset: 1

Author

N. J. A. Sloane, based on correspondence from Toru Ito (t_ito(AT)mue.biglobe.ne.jp), Nov 06 2004

Keywords

• hard
• nonn
• nice
• more

Comments

There are at least two ways to define Latin cubes - see the Preece et al. paper. - Rosemary Bailey, Nov 03 2004

References

• T. Ito, Method for producing Latin squares, Publication number JP2000-28510A, Japan Patent Office.
• T. Ito, Method for producing Latin squares, JP3394467B, Patent abstracts of Japan, Japan Patent Office.
• Jia, Xiong Wei and Qin, Zhong Ping, The number of Latin cubes and their isotopy classes, J. Huazhong Univ. Sci. Tech. 27 (1999), no. 11, 104-106. MathSciNet #MR1751724.

Links

• B. D. McKay and I. M. Wanless, A census of small latin hypercubes, SIAM J. Discrete Math. 22, (2008) 719-736.
• Gary L. Mullen, and Robert E. Weber, Latin cubes of order <= 5, Discrete Math. 32 (1980), no. 3, 291-297. (Gives a(1)-a(5).)
• D. A. Preece, S. C. Pearce and J. R. Kerr, Orthogonal designs for three-dimensional experiments, Biometrika 60 (1973), 349-358.

Crossrefs

Cf. A098843, A098846, A099321; A002860 (Latin squares).

A row of the array in A249026.

Formula

a(n) = n!*(n-1)!*(n-1)!*A098843(n).

Extensions

a(6) computed independently by Brendan McKay and Ian Wanless, Dec 17 2004