A091261 Number of orthogonal mates for the cyclic Latin squares of odd order.

1, 3, 635, 2049219, 7372235460687

Offset

3,2

Comments

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.

Links

Table of n, a(n) for n=3..7.

N. J. Cavenagh and I. M. Wanless, On the number of transversals in Cayley tables of cyclic groups, Disc. Appl. Math. 158 (2010), 136-146.

B. M. Maenhaut and I. M. Wanless, Atomic Latin squares of order eleven, J. Combin. Designs, Vol. 12 (2004), pp. 12-34.

Formula

a(n) grows at least exponentially in n [Cavenagh, Wanless]. - Ian Wanless, Jul 30 2010

Crossrefs

Cf. A001438.

Sequence in context: A161964 A229688 A287890 * A332163 A230808 A158600

Adjacent sequences: A091258 A091259 A091260 * A091262 A091263 A091264

Keyword

hard,nonn

Author

Ian Wanless, Feb 23 2004

Status

approved