

A098679


Total number of Latin cubes of order n.


8




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 JP200028510A, 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, 104106. 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) 719736.
Gary L. Mullen, and Robert E. Weber, Latin cubes of order <= 5, Discrete Math. 32 (1980), no. 3, 291297. (Gives a(1)a(5).)
D. A. Preece, S. C. Pearce and J. R. Kerr, Orthogonal designs for threedimensional experiments, Biometrika 60 (1973), 349358.


FORMULA

a(n) = n!*(n1)!*(n1)!*A098843(n).


CROSSREFS

Cf. A098843, A098846, A099321; A002860 (Latin squares).
A row of the array in A249026.
Sequence in context: A229333 A108349 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



