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 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 (list; graph; refs; listen; history; text; internal format)
 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 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 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: 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

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Last modified May 26 14:46 EDT 2020. Contains 334626 sequences. (Running on oeis4.)