1,2

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

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.

B. D. McKay and I. M. Wanless, A census of small latin hypercubes, SIAM J. Discrete Math. 22, (2008) 719-736.

Mullen, Gary L.; and Weber, Robert E., 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.

Equals n!*(n-1)!*(n-1)!*A098843.

Cf. A098843, A098846, A099321.

Sequence in context: A137888 A108349 A000722 this_sequence A123851 A120122 A068943

Adjacent sequences: A098676 A098677 A098678 this_sequence A098680 A098681 A098682

hard,nonn,nice

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

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