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

Author

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

Keywords

• nonn
• changed

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

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

Links

• Denis S. Krotov and Vladimir 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.
• Denis S. Krotov and Vladimir N. Potapov, n-Ary Quasigroups of Order 4, arXiv:math/0701519 [math.CO], 2007-2008; SIAM J. Discrete Math. 23:2 (2009), 561-570.
• B. D. McKay and I. M. Wanless, A census of small latin hypercubes, SIAM J. Discrete Math. 22, (2008) 719-736.
• Vladimir N. Potapov and Denis S. Krotov, On the number of n-ary quasigroups of finite order, arXiv:0912.5453 [math.CO], 2009-2016; Discrete Mathematics and Applications, 21:5-6 (2011), 575-586.

Crossrefs

Cf. A002860, A098679, A100540, A132206.

Programs

Python

# See A211214.

Formula

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