OFFSET
1,2
COMMENTS
Number of Eulerian circuits in the Cartesian product of two directed cycles of lengths 5 and n. - Andrew Howroyd, Jan 12 2018
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.
FORMULA
From Andrew Howroyd, Jan 12 2018: (Start)
Empirical: a(n) = 121*a(n-1) - 6520*a(n-2) + 209330*a(n-3) - 4493120*a(n-4) + 68446433*a(n-5) - 766303183*a(n-6) + 6438802040*a(n-7) - 41070618160*a(n-8) + 199602863240*a(n-9) - 736417358863*a(n-10) + 2039087685503*a(n-11) - 4149490675520*a(n-12) + 5992940178830*a(n-13) - 5786524000120*a(n-14) + 3329026307431*a(n-15) - 852891037441*a(n-16) for n > 16.
Empirical g.f.: x*(1 - 31*x^2)*(1 - 2479*x^2 + 94380*x^3 - 1719180*x^4 + 18597458*x^5 - 128373600*x^6 + 576521198*x^7 - 1652131980*x^8 + 2811674580*x^9 - 2289408559*x^10 + 887503681*x^12)/((1 - x)*(1 - 31*x)*(1 - 12*x + 31*x^2)*(1 - 9*x + 31*x^2 - 49*x^3 + 31*x^4)*(1 - 19*x + 151*x^2 - 589*x^3 + 961*x^4)*(1 - 49*x + 961*x^2 - 8649*x^3 + 29791*x^4)).
(End)
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[5, n] // Round;
Array[a, 20] (* Jean-François Alcover, Jul 04 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 27 2012
STATUS
approved