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A055495
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Numbers n such that there exists a pair of mutually orthogonal Latin squares of order n.
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1
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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
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1,1
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COMMENTS
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n such that there exists a pair of orthogonal 1-factorizations of K_{n,n}.
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REFERENCES
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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.
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LINKS
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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
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FORMULA
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All n >= 3 except 6.
G.f.: -(x^4-x^3+2*x-3)*x/(x-1)^2. - Alois P. Heinz, Dec 14 2017
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CROSSREFS
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Sequence in context: A231346 A033545 A253570 * A072442 A063992 A324540
Adjacent sequences: A055492 A055493 A055494 * A055496 A055497 A055498
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Dec 07 2000
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STATUS
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approved
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