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A054884
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Number of closed walks of length n along the edges of an icosahedron based at a vertex.
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2
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1, 0, 5, 10, 65, 260, 1365, 6510, 32865, 162760, 815365, 4069010, 20352865, 101725260, 508665365, 2543131510, 12715852865, 63578287760, 317892415365, 1589457194010, 7947290852865, 39736429850260
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OFFSET
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0,3
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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 * A030517(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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MATHEMATICA
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LinearRecurrence[{4, 10, -20, -25}, {1, 0, 5, 10}, 30] (* Harvey P. Dale, May 02 2022 *)
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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, A054885.
Sequence in context: A240647 A062162 A062848 * A061518 A218540 A174937
Adjacent sequences: A054881 A054882 A054883 * A054885 A054886 A054887
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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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