A282621 Number of Eulerian cycles in the graph C_3 X C_n.

8, 320, 8616, 207496, 4788808, 108326760, 2423906696, 53891103656, 1193490502728, 26367062410600, 581618469479176, 12817206071979816, 282280911579925448, 6214413253138283240, 136776355872474130056, 3009909527048881143976, 66229625352973066928968

Offset: 1

Author

Andrew Howroyd, Jan 14 2018

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Eulerian Cycle
• Eric Weisstein's World of Mathematics, Torus Grid Graph
• Index entries for linear recurrences with constant coefficients, signature (47, -742, 4796, -13144, 12320).

Crossrefs

Row 3 of A298117.

Programs

Mathematica

Table[22^n + 1/3 (2^n + 3 2^(1 + 2 n) - 8 5^n - 2^(1 + n) 7^n), {n, 20}] (* Eric W. Weisstein, Jan 15 2018 *)
LinearRecurrence[{47, -742, 4796, -13144, 12320}, {8, 320, 8616, 207496, 4788808}, 20] (* Eric W. Weisstein, Jan 15 2018 *)
CoefficientList[Series[8 (1 - 7 x - 61 x^2 + 202 x^3)/((1 - 2 x) (1 - 4 x) (1 - 5 x) (1 - 14 x) (1 - 22 x)), {x, 0, 20}], x] (* Eric W. Weisstein, Jan 15 2018 *)

PARI

Vec(8*(1 - 7*x - 61*x^2 + 202*x^3)/((1 - 2*x)*(1 - 4*x)*(1 - 5*x)*(1 - 14*x)*(1 - 22*x)) + O(x^20))

Formula

a(n) = 47*a(n-1) - 742*a(n-2) + 4796*a(n-3) - 13144*a(n-4) + 12320*a(n-5) for n > 5.

G.f.: 8*x*(1 - 7*x - 61*x^2 + 202*x^3)/((1 - 2*x)*(1 - 4*x)*(1 - 5*x)*(1 - 14*x)*(1 - 22*x)).

a(n) = 22^n + (2^n + 3*2^(1 + 2*n) - 8*5^n - 2^(1 + n)*7^n)/3. - Eric W. Weisstein, Jan 15 2018