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

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

Author

N. J. A. Sloane, Dec 07 2000

Keywords

• nonn
• easy

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

• 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).

Crossrefs

Cf. A000027.

Formula

All k >= 3 except 6.

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