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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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1
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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.: -1/5-1/4/(t-1)-1/20/(3*t-1)+1/5/(2*t+1)+3/10/(5*t^2-1).
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 / ((x-1)*(2*x+1)*(3*x-1)*(5*x^2-1)). - Colin Barker, Dec 21 2014
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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
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CROSSREFS
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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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