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