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