A006240 - OEIS

%I M5271 #31 Jul 04 2018 03:16:27

%S 1,40,793,12800,193721,2886520,42999713,642355200,9617422321,

%T 144167168200,2162192792233,32433400563200,486521516676521,

%U 7298047169453080,109472483776866353,1642098503032012800,24631532723767204321,369473147671033293160,5542096617629211606073,83131435057615545920000

%N Row 4 of array in A212801.

%C Number of Eulerian circuits in the Cartesian product of two directed cycles of lengths 4 and n. - _Andrew Howroyd_, Jan 14 2018

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Andrew Howroyd, <a href="/A006240/b006240.txt">Table of n, a(n) for n = 1..200</a>

%H Germain Kreweras, <a href="http://dx.doi.org/10.1016/0095-8956(78)90021-7">Complexité et circuits Eulériens dans les sommes tensorielles de graphes</a>, J. Combin. Theory, B 24 (1978), 202-212.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Checkers.html">Checkers</a>.

%F 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

%F 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

%t 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}];

%t a[n_] := T[4, n] // Round;

%t Array[a, 20] (* _Jean-François Alcover_, Jul 04 2018 *)

%Y Cf. A212801.

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E Revised by _N. J. A. Sloane_, May 27 2012