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A098679
Total number of Latin cubes of order n.
8
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
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
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