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 A006239 Row 3 of array in A212801. (Formerly M4909) 2
 1, 13, 108, 793, 5611, 39312, 274933, 1923025, 13455396, 94169413, 659134543, 4613813568, 32296413241, 226074381637, 1582520088348, 11077641280225, 77543496352291, 542804506787088, 3799631657379853, 26597421924762793 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of Eulerian circuits in the Cartesian product of two directed cycles of lengths 3 and n. - Andrew Howroyd, Jan 14 2018 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 Germain Kreweras, Complexité et circuits Eulériens dans les sommes tensorielles de graphes, J. Combin. Theory, B 24 (1978), 202-212. See p. 211. Eric Weisstein's World of Mathematics, Checkers. FORMULA Empirical g.f.: x*(1-7*x^2)/((1-x)*(1-7*x)*(1-5*x+7*x^2)). - Bruno Berselli, May 31 2012 Empirical closed form: a(n) = (2^n*(1+7^n) -(5-i*sqrt(3))^n -(5+i*sqrt(3))^n) / (3*2^n), where i=sqrt(-1). - Bruno Berselli, May 31 2012 MATHEMATICA T[m_, n_] := Product[2 - Exp[2*I*h*Pi/m] - Exp[2*I*k*Pi/n], {h, 1, m - 1}, {k, 1, n - 1}]; a[n_] := T[3, n] // Round; Array[a, 20] (* Jean-François Alcover, Jul 04 2018 *) CROSSREFS Cf. A212801. Sequence in context: A038384 A038385 A084901 * A271560 A142040 A002648 Adjacent sequences: A006236 A006237 A006238 * A006240 A006241 A006242 KEYWORD nonn AUTHOR EXTENSIONS Revised by N. J. A. Sloane, May 27 2012 STATUS approved

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Last modified December 3 17:38 EST 2022. Contains 358535 sequences. (Running on oeis4.)