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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: A033545 A253570 A362580 * A072442 A063992 A324540
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 07 2000
STATUS
approved

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Last modified March 29 09:14 EDT 2024. Contains 371268 sequences. (Running on oeis4.)