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%I #14 Jun 29 2023 16:12:01
%S 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,
%T 29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,
%U 52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67
%N Numbers n such that there exists a pair of mutually orthogonal Latin squares of order n.
%C n such that there exists a pair of orthogonal 1-factorizations of K_{n,n}.
%D 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.
%H R. C. Bose, S. S. Shrikhande, E. T. Parker, <a href="http://dx.doi.org/10.4153/CJM-1960-016-5">Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler's conjecture</a>, Canad. J. Math. 12(1960), 189-203.
%H Peter Cameron's Blog, <a href="https://cameroncounts.wordpress.com/2010/08/26/the-shrikhande-graph/">The Shrikhande graph</a>, 28 August 1010.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EulersGraeco-RomanSquaresConjecture.html">Euler's Graeco-Roman Squares Conjecture</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).
%F All n >= 3 except 6.
%F G.f.: -(x^4-x^3+2*x-3)*x/(x-1)^2. - _Alois P. Heinz_, Dec 14 2017
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Dec 07 2000
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