A054883 Number of walks of length n along the edges of a dodecahedron between two opposite vertices.

0, 0, 0, 0, 0, 6, 12, 84, 192, 882, 2220, 8448, 22704, 78078, 218988, 710892, 2048256, 6430794, 18837516, 58008216, 171619248, 522598230, 1555243404, 4705481220, 14051590080, 42357719586, 126740502252, 381253030704, 1142062255152, 3431411494062

Offset

0,6

Links

Colin Barker, 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-t) + 1/(1-3*t) + 4/(1+2*t) - 6/(1-5*t^2)).

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

G.f.: 6*x^5/((1-x)*(1+2*x)*(1-3*x)*(1-5*x^2)). - Colin Barker, Dec 21 2014

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

Mathematica

LinearRecurrence[{2, 10, -16, -25, 30}, {0, 0, 0, 0, 0, 6}, 30] (* Harvey P. Dale, Nov 13 2021 *)

Prog

(PARI) concat([0, 0, 0, 0, 0], Vec(-6*x^5/((x-1)*(2*x+1)*(3*x-1)*(5*x^2-1)) + O(x^100))) \\ Colin Barker, Dec 21 2014
(Magma) [Round((5 +3^n +4*(-2)^n -3*(1+(-1)^n)*5^(n/2))/20): n in [0..30]]; // G. C. Greubel, Feb 07 2023
(SageMath)
def A054883(n): return (5 +3^n +4*(-2)^n -3*(1+(-1)^n)*5^(n/2))/20 -int(n==0)/5
[A054883(n) for n in range(41)] # G. C. Greubel, Feb 07 2023

Crossrefs

Cf. A054881, A054882, A054884, A054885.

Sequence in context: A196253 A338563 A345271 * A005402 A128953 A181597

Adjacent sequences: A054880 A054881 A054882 * A054884 A054885 A054886

Keyword

nonn,easy

Author

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

Status

approved