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 A006240 Row 4 of array in A212801. (Formerly M5271) 3
 1, 40, 793, 12800, 193721, 2886520, 42999713, 642355200, 9617422321, 144167168200, 2162192792233, 32433400563200, 486521516676521, 7298047169453080, 109472483776866353, 1642098503032012800, 24631532723767204321, 369473147671033293160, 5542096617629211606073, 83131435057615545920000 (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 4 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. Eric Weisstein's World of Mathematics, Checkers. FORMULA Empirical g.f.: x*(1-167*x^2+1200*x^3-2505*x^4+3375*x^6)/((1-x)*(1-3*x)*(1-5*x)*(1-15*x)*(1-4*x+5*x^2)*(1-12*x+45*x^2)). - Bruno Berselli, May 31 2012 Empirical closed form: a(n) = (15^n+3^n-5^n-1+(2+i)^n+(2-i)^n -(6+3*i)^n -(6-3*i)^n)/4, 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[4, n] // Round; Array[a, 20] (* Jean-François Alcover, Jul 04 2018 *) CROSSREFS Cf. A212801. Sequence in context: A022073 A261571 A010956 * A126928 A035715 A035609 Adjacent sequences:  A006237 A006238 A006239 * A006241 A006242 A006243 KEYWORD nonn AUTHOR EXTENSIONS Revised by N. J. A. Sloane, May 27 2012 STATUS approved

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Last modified December 4 18:08 EST 2021. Contains 349526 sequences. (Running on oeis4.)