A098679 Total number of Latin cubes of order n.

1, 2, 24, 55296, 2781803520, 994393803303936000

Offset

1,2

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

Table of n, a(n) for n=1..6.

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.

Formula

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

Crossrefs

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

A row of the array in A249026.

Sequence in context: A108349 A361431 A000722 * A123851 A258824 A120122

Adjacent sequences: A098676 A098677 A098678 * A098680 A098681 A098682

Keyword

hard,nonn,nice,more

Author

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

Extensions

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

Status

approved