A375309 Number of walks of length n along the edges of a dodecahedron graph between two vertices at distance two.

0, 0, 1, 1, 7, 11, 51, 105, 399, 967, 3299, 8789, 28271, 79443, 247507, 716353, 2193583, 6452639, 19575075, 58095597, 175350735, 522947755, 1574075603, 4706879321, 14146450127, 42363311991, 127217598691, 381275400325, 1144458922159

Offset: 0

Author

Miquel A. Fiol, Aug 11 2024

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,10,-16,-25,30).

Crossrefs

Cf. A054883.

Programs

Mathematica

LinearRecurrence[{2, 10, -16, -25, 30}, {0, 0, 1, 1, 7, 11}, 30] (* Amiram Eldar, Aug 13 2024 *)

Formula

For n>=6, a(n) = 2*a(n-1) + 10*a(n-2) - 16*a(n-3) - 25*a(n-4) + 30*a(n-5).

From Stefano Spezia, Aug 13 2024: (Start)

G.f.: x^2*(1 - x - 5*x^2 + 3*x^3)/((1 - x)*(1 + 2*x)*(1 - 3*x)*(1 - 5*x^2)).

a(n) = (3*5^(n/2)*(1 + (-1)^n) + 3^(1+n) + (-1)^n*2^(1+n) - 5)/60 for n > 0. (End)