A211215 Total number of Latin n-dimensional hypercubes of order 4; labeled n-ary quasigroups of order 4.

4, 24, 576, 55296, 36972288, 6268637952000, 80686060158523011084288, 4465185218736554544676917926460256725000192, 4558271384916189349044295395852008182480786230841798008741684281906576963885826048

Offset

0,1

Comments

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.

References

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, http://www.ict.nsc.ru/ws/Lyap2001/2363/

T. Ito, Creation Method of Table, Creation Apparatus, Creation Program and Program Storage Medium, U.S. Patent application 20040243621, Dec 02 2004

B. D. McKay, I. M. Wanless, A census of small latin hypercubes, SIAM J. Discrete Math. 22:2 (2008) 719-736

Links

Table of n, a(n) for n=0..8.

D. S. Krotov, V. N. Potapov, n-Ary Quasigroups of Order 4, SIAM J. Discrete Math. 23:2 (2009), 561-570, arXiv: math/0701519

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

Formula

a(n) = 4*6^n * A211214(n).

Prog

See A211214.

Crossrefs

Cf. A002860, A098679, A100540, A132206.

Sequence in context: A013100 A013061 A071302 * A249028 A216092 A174245

Adjacent sequences: A211212 A211213 A211214 * A211216 A211217 A211218

Keyword

nonn

Author

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

Status

approved