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
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.
Programs
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Python
# See A211214.
Formula
a(n) = 4*6^n * A211214(n).
Comments