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

%I #10 Dec 16 2016 10:46:40

%S 1,2,96,6268637952000,2010196727432478720

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

%C 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.

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

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

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

%F 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).

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

%Y Cf. A100540, A132205.

%Y A row of the array in A249026.

%K nonn,more

%O 1,2

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

%E a(5) from _Ian Wanless_, May 01 2008

%E Edited by _N. J. A. Sloane_, Dec 05 2009 at the suggestion of Vladeta Jovovic