A098843 Number of reduced Latin cubes of order n.

1, 1, 1, 64, 40246, 95909896152

Offset

1,4

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.

Crossrefs

Cf. A098846 (isomorphism classes), A098679 (total number), A099321 (isotopy classes).

Sequence in context: A202911 A013743 A223353 * A159400 A221615 A141092

Adjacent sequences: A098840 A098841 A098842 * A098844 A098845 A098846

Keyword

hard,nonn,nice,more

Author

N. J. A. Sloane, based on correspondence from Toru Ito (t_ito(AT)mue.biglobe.ne.jp), Nov 03 2004

Extensions

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

Status

approved