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 A090741 Maximum number of transversals in a Latin square of order n. 2
 1, 0, 3, 8, 15, 32, 133, 384, 2241 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(10) >= 5504 from Parker. REFERENCES D. Bedford, Transversals in the Cayley tables of the non-cyclic groups of order 8, European Journal of Combinatorics, volume 12 (1991), 455-458. N. J. Cavenagh and I. M. Wanless, On the number of transversals in Cayley tables of cyclic groups, Disc. Appl. Math. 158 (2010), 136-146. B. D. McKay, J. C. McLeod and I. M. Wanless, The number of transversals in a Latin square, Des. Codes Cryptogr., 40, (2006) 269-284. E. T. Parker, Computer investigations of orthogonal Latin squares of order 10, Proc. Sympos. Appl. Math., volume 15 (1963), 73-81. LINKS Ian M. Wanless, A Generalization of Transversals for Latin Squares, Electronic Journal of Combinatorics, volume 9, number 1 (2002), R12. FORMULA a(n) is asymptotically in between 3.2^n and 0.62^n n!. [McKay, McLeod, Wanless], [Cavenagh, Wanless] - From Ian Wanless, Jul 30 2010 EXAMPLE a(1), a(3), a(5), a(7) are from the group tables for Z_1, Z_3, Z_5 and Z_7 (see sequence A006717); a(4) and a(8) are from Z_2 x Z_2 and the non-cyclic groups of order 8 (see Bedford). a(9) = 2241 from Z_3 x Z_3. CROSSREFS Cf. A006717, A091325. Sequence in context: A135350 A068038 A196087 * A032234 A032255 A137475 Adjacent sequences:  A090738 A090739 A090740 * A090742 A090743 A090744 KEYWORD hard,nonn AUTHOR Richard Bean (rwb(AT)eskimo.com), Feb 03 2004 EXTENSIONS a(9) = 2241 from Brendan McKay and Ian Wanless, May 23, 2004 STATUS approved

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