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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
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
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
KEYWORD
nonn
EXTENSIONS
Revised by N. J. A. Sloane, May 27 2012
STATUS
approved