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A375309
Number of walks of length n along the edges of a dodecahedron graph between two vertices at distance two.
0
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
0,5
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)
MATHEMATICA
LinearRecurrence[{2, 10, -16, -25, 30}, {0, 0, 1, 1, 7, 11}, 30] (* Amiram Eldar, Aug 13 2024 *)
CROSSREFS
Cf. A054883.
Sequence in context: A003599 A018508 A038277 * A045462 A263231 A077411
KEYWORD
nonn,easy
AUTHOR
Miquel A. Fiol, Aug 11 2024
STATUS
approved