|
|
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
|
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;
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|