A132206 Total number of Latin 5-dimensional hypercubes (Latin polyhedra) of order n.

1, 2, 96, 6268637952000, 2010196727432478720

Offset

1,2

Comments

L5(1) = 1, L5(2) = 1, L5(3) = 1, L5(4) = 201538000 L5(1)~l5(4) are Number of reduced Latin 5-dimensional hypercubes (Latin polyhedra) of order n. Latin 5-dimensional hypercubes (Latin polyhedra) are a generalization of Latin cube and Latin square. a(4) and L5(4) computed on Dec 01 2002.

References

T. Ito, Method, equipment, program and storage media for producing tables, Publication number JP2004-272104A, Japan Patent Office (written in Japanese).

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

Kenji Ohkuma, Atsuhiro Yamagishi and Toru Ito, Cryptography Research Group Technical report, IT Security Center, Information-Technology Promotion Agency, JAPAN.

Links

Table of n, a(n) for n=1..5.

Formula

Equals n*(n-1)!^5*L5(n), where L5(n) is number of reduced Latin 5-dimensional hypercubes (Latin polyhedra) of order n (cf. A132205).

Example

4*(4-1)!^5*L5(4) = 6268637952000 where L5(4) = 201538000

Crossrefs

Cf. A100540, A132205.

A row of the array in A249026.

Sequence in context: A346565 A224986 A164335 * A139884 A297423 A189313

Adjacent sequences: A132203 A132204 A132205 * A132207 A132208 A132209

Keyword

nonn,more

Author

Toru Ito (to-itou(AT)ipa.go.jp), Nov 06 2007

Extensions

a(5) from Ian Wanless, May 01 2008

Edited by N. J. A. Sloane, Dec 05 2009 at the suggestion of Vladeta Jovovic

Status

approved