A054882 Closed walks of length n along the edges of a dodecahedron based at a vertex.

1, 0, 3, 0, 15, 6, 87, 84, 567, 882, 4095, 8448, 32079, 78078, 265863, 710892, 2282631, 6430794, 20009391, 58008216, 177478623, 522598230, 1584540279, 4705481220, 14198074455, 42357719586, 127472924127, 381253030704

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (1/20)*(4 + 5/(1-x) + 1/(1-3*x) + 4/(1+2*x) + 6/(1-5*x^2)).

G.f.: (1 - 2*x - 7*x^2 + 10*x^3 + 10*x^4 - 6*x^5)/((1-x)*(1+2*x)*(1-3*x)*(1-5*x^2)).

a(n) = (5 + 3^n + (-1)^n*2^(n+2) + 3*(1+(-1)^n)*sqrt(5)^n + 4*0^n)/20.

E.g.f.: (1/20)*(4 + 4*exp(-2*x) + 5*exp(x) + exp(3*x) + 6*cosh(sqrt(5)*x)). - G. C. Greubel, Feb 07 2023

Mathematica

LinearRecurrence[{2, 10, -16, -25, 30}, {1, 0, 3, 0, 15, 6}, 41] (* G. C. Greubel, Feb 07 2023 *)

Prog

(Magma) [Ceiling((5+3^n+(-1)^n*2^(n+2)+3*(1+(-1)^n)*Sqrt(5)^n)/20): n in [0..30]]; // Vincenzo Librandi, Aug 24 2011
(SageMath)
def A054882(n): return (5+3^n+4*(-2)^n+3*(1+(-1)^n)*5^(n/2)+4*0^n)/20
[A054882(n) for n in range(41)] # G. C. Greubel, Feb 07 2023

Crossrefs

Cf. A054881, A054883, A054884, A054885.

Sequence in context: A130637 A365419 A366410 * A303232 A086479 A091000

Adjacent sequences: A054879 A054880 A054881 * A054883 A054884 A054885

Keyword

nonn,easy,walk

Author

Paolo Dominici (pl.dm(AT)libero.it), May 23 2000

Status

approved