A006240 Row 4 of array in A212801.

1, 40, 793, 12800, 193721, 2886520, 42999713, 642355200, 9617422321, 144167168200, 2162192792233, 32433400563200, 486521516676521, 7298047169453080, 109472483776866353, 1642098503032012800, 24631532723767204321, 369473147671033293160, 5542096617629211606073, 83131435057615545920000

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Cf. A212801.

Programs

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 *)

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

Extensions

Revised by N. J. A. Sloane, May 27 2012