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A160368 Number of self-orthogonal Latin squares of order n. 10
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

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Last modified May 21 18:43 EDT 2019. Contains 323444 sequences. (Running on oeis4.)