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%I #9 Dec 17 2016 10:26:56
%S 1,3,635,2049219,7372235460687
%N Number of orthogonal mates for the cyclic Latin squares of odd order.
%C It is well known that the Cayley table of the cyclic group of order n has no orthogonal mate whenever n is even. This sequence reports the number of standardized orthogonal mates when n is odd, starting at n=3 (the case n=1 being meaningless). The word "standardized" refers to the fact that we only count mates which have their first row in natural order, since relabeling of the symbols in the orthogonal mate does not affect its defining property.
%H N. J. Cavenagh and I. M. Wanless, <a href="http://dx.doi.org/10.1016/j.dam.2009.09.006">On the number of transversals in Cayley tables of cyclic groups</a>, Disc. Appl. Math. 158 (2010), 136-146.
%H B. M. Maenhaut and I. M. Wanless, <a href="http://users.monash.edu.au/~iwanless/abstracts/atomic11.html">Atomic Latin squares of order eleven</a>, J. Combin. Designs, Vol. 12 (2004), pp. 12-34.
%F a(n) grows at least exponentially in n [Cavenagh, Wanless]. - _Ian Wanless_, Jul 30 2010
%Y Cf. A001438.
%K hard,nonn
%O 3,2
%A _Ian Wanless_, Feb 23 2004