A055495 Numbers n such that there exists a pair of mutually orthogonal Latin squares of order n.

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

Offset

1,1

Comments

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

References

B. Alspach, K. Heinrich and G. Liu, Orthogonal factorizations of graphs, pp. 13-40 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), 189-203.

Peter Cameron's Blog, The Shrikhande graph, 28 August 1010.

Eric Weisstein's World of Mathematics, Euler's Graeco-Roman Squares Conjecture

Index entries for linear recurrences with constant coefficients, signature (2, -1).

Formula

All n >= 3 except 6.

G.f.: -(x^4-x^3+2*x-3)*x/(x-1)^2. - Alois P. Heinz, Dec 14 2017

Crossrefs

Sequence in context: A033545 A253570 A362580 * A072442 A063992 A324540

Adjacent sequences: A055492 A055493 A055494 * A055496 A055497 A055498

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 07 2000

Status

approved