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A160368

Number of self-orthogonal Latin squares of order n.

1, 0, 0, 48, 1440, 0, 19353600, 4180377600, 25070769561600, 3200285563453440000 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,4`
	COMMENTS	`A self-orthogonal Latin square is a Latin square orthogonal to its transpose and a SOLS L is idempotent if L(i,i)=i. The number of distinct SOLS of order n may be determined by multiplying the number of idempotent SOLS of order n by n!.`
	REFERENCES	`G. P. Graham and C.E. Roberts, 2006. Enumeration and isomorphic classification of self-orthogonal Latin squares, Journal of Combinatorial Mathematics and Combinatorial Computing, 59, pp. 101-118.`
	LINKS	`Table of n, a(n) for n=1..10.` `A. P. Burger, M. P. Kidd and J. H. van Vuuren, 2010. Enumerasie van self-ortogonale Latynse vierkante van orde 10, LitNet Akademies (Natuurwetenskappe), 7(3), pp 1-22.` `A. P. Burger, M. P. Kidd and J. H. van Vuuren, Enumeration of isomorphism classes of self-orthogonal Latin squares, Ars Combinatoria, 97, pp. 143-152.` `M. P. Kidd, A repository of self-orthogonal Latin squares`
	CROSSREFS	`Cf. A160365, A160366, n!A160367.` `Sequence in context: A174113 A089272 A004362 A275042 A062195 A264322` `Adjacent sequences: A160365 A160366 A160367 * A160369 A160370 A160371`
	KEYWORD	`hard,more,nonn`
	AUTHOR	`Martin P Kidd, May 11 2009`
	EXTENSIONS	`References updated and a link updated by Martin P Kidd, Aug 14 2010`
	STATUS	`approved`

Last modified August 6 02:23 EDT 2024. Contains 374957 sequences. (Running on oeis4.)