

A055495


Numbers n such that there exists a pair of mutually orthogonal Latin squares of order n.


1



3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67
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OFFSET

1,1


COMMENTS

n such that there exists a pair of orthogonal 1factorizations of K_{n,n}.


REFERENCES

B. Alspach, K. Heinrich and G. Liu, Orthogonal factorizations of graphs, pp. 1340 of Contemporary Design Theory, ed. J. H. Dinizt and D. R. Stinson, Wiley, 1992.


LINKS

Table of n, a(n) for n=1..64.
R. C. Bose, S. S. Shrikhande, E. T. Parker, Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler's conjecture, Canad. J. Math. 12(1960), 189203.
Peter Cameron's Blog, The Shrikhande graph, 28 August 1010.
Eric Weisstein's World of Mathematics, Euler's GraecoRoman Squares Conjecture


FORMULA

All n >= 3 except 6.
G.f.: (x^4x^3+2*x3)*x/(x1)^2.  Alois P. Heinz, Dec 14 2017


CROSSREFS

Sequence in context: A231346 A033545 A253570 * A072442 A063992 A324540
Adjacent sequences: A055492 A055493 A055494 * A055496 A055497 A055498


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Dec 07 2000


STATUS

approved



