A100539 -id:A100539 - cp's OEIS frontend

A100540 Total number of Latin 4-dimensional hypercubes (Latin polyhedra) of order n.

Original entry on oeis.org

1, 2, 48, 36972288, 52260618977280

Offset: 1

Toru Ito (t_ito(AT)mue.biglobe.ne.jp), Nov 28 2004

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

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

Cf. A100539, A132205, A132206.

A row of the array in A249026.

a(5) from Ian Wanless, May 01 2008

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

A211214 Number of reduced Latin n-dimensional hypercubes of order 4; labeled n-ary loops of order 4 with fixed identity.

Original entry on oeis.org

1, 1, 4, 64, 7132, 201538000, 432345572694417712, 3987683987354747642922773353963277968, 678469272874899582559986240285280710364867063489779510427038722229750276832

Offset: 0

Denis S. Krotov and Vladimir N. Potapov, Apr 06 2012

The values are calculated recursively, based on the characterization by 2009. The number a(5) was found before (2001 and, independently, later works) by exhaustive computer-aided classification of the objects.

T. Ito, Creation Method of Table, Creation Apparatus, Creation Program and Program Storage Medium, U.S. Patent US7228311B2 and Patent application 20040243621, Dec. 2, 2004.
D. S. Krotov, V. N. Potapov, On the reconstruction of N-quasigroups of order 4 and the upper bounds on their numbers, Proc. Conference devoted to the 90th anniversary of Alexei A. Lyapunov (Novosibirsk, Russia, October 8-11, 2001), 2001.
D. S. Krotov, V. N. Potapov, n-Ary Quasigroups of Order 4, SIAM J. Discrete Math. 23:2 (2009), 561-570, arXiv: math/0701519.
B. D. McKay, I. M. Wanless, A census of small latin hypercubes, SIAM J. Discrete Math. 22:2 (2008) 719-736.
V. N. Potapov, D. S. Krotov, On the number of n-ary quasigroups of finite order, Discrete Mathematics and Applications, 21:5-6 (2011), 575-586, arXiv:0912.5453.

Cf. A000315, A098843, A100539, A132205.

a(n) = A211215(n)/(4*6^n).

cp's OEIS Frontend

A100540 Total number of Latin 4-dimensional hypercubes (Latin polyhedra) of order n.

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