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A054883
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Number of walks of length n along the edges of a dodecahedron between two opposite vertices.
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5
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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
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OFFSET
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0,6
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LINKS
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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).
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FORMULA
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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
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MATHEMATICA
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LinearRecurrence[{2, 10, -16, -25, 30}, {0, 0, 0, 0, 0, 6}, 30] (* Harvey P. Dale, Nov 13 2021 *)
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PROG
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(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
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CROSSREFS
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Cf. A054881, A054882, A054884, A054885.
Sequence in context: A196253 A338563 A345271 * A005402 A128953 A181597
Adjacent sequences: A054880 A054881 A054882 * A054884 A054885 A054886
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KEYWORD
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nonn,easy
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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STATUS
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approved
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