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A054885
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Number of walks of length n along the edges of an icosahedron between two opposite vertices.
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2
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0, 0, 0, 10, 40, 260, 1240, 6510, 32240, 162760, 812240, 4069010, 20337240, 101725260, 508587240, 2543131510, 12715462240, 63578287760, 317890462240, 1589457194010, 7947281087240, 39736429850260
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OFFSET
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0,4
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,10,-20,-25).
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FORMULA
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G.f.: -(1/12)/(5*t-1) + (5/12)/(t+1) + (1/2)/(5*t^2-1).
a(n) = (5^n + (-1)^n*5 - 3*(1 + (-1)^n)*sqrt(5)^n)/12.
a(n+1) = 5 * A030518(n) for n > 0.
a(n) = 4*a(n-1) + 10*a(n-2) - 20*a(n-3) - 25*a(n-4). - François Marques, Jul 10 2021
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PROG
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(MAGMA) [Floor((5^n+(-1)^n*5-3*(1+(-1)^n)*Sqrt(5)^n)/12): n in [0..30]]; // Vincenzo Librandi, Aug 24 2011
(PARI) a(n) = if(n%2, 5^n-5, 5^n+5-6*5^(n/2))/12; \\ François Marques, Jul 11 2021
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CROSSREFS
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Cf. A030517, A030518, A054884.
Sequence in context: A061991 A060580 A118266 * A000449 A027274 A253674
Adjacent sequences: A054882 A054883 A054884 * A054886 A054887 A054888
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KEYWORD
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nonn,walk,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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