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A054882 Closed walks of length n along the edges of a dodecahedron based at a vertex. 1
1, 0, 3, 0, 15, 6, 87, 84, 567, 882, 4095, 8448, 32079, 78078, 265863, 710892, 2282631, 6430794, 20009391, 58008216, 177478623, 522598230, 1584540279, 4705481220, 14198074455, 42357719586, 127472924127, 381253030704 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,10,-16,-25,30).

FORMULA

G.f.: 1/5 - (1/4)/(x-1) - (1/20)/(3*x-1) + (1/5)/(2*x+1) - (3/10)/(5*x^2-1) = (1 - 2*x - 7*x^2 + 10*x^3 + 10*x^4 - 6*x^5)/((1-x)*(1+2*x)*(1-3*x)*(1-5*x^2)).

a(n) = (5 + 3^n + (-1)^n*2^(n+2) + 3*(1+(-1)^n)*sqrt(5)^n)/20 for n > 0.

PROG

(MAGMA) [Ceiling((5+3^n+(-1)^n*2^(n+2)+3*(1+(-1)^n)*Sqrt(5)^n)/20): n in [0..30]]; // Vincenzo Librandi, Aug 24 2011

CROSSREFS

Sequence in context: A138540 A123023 A130637 * A303232 A086479 A091000

Adjacent sequences:  A054879 A054880 A054881 * A054883 A054884 A054885

KEYWORD

nonn,easy,walk

AUTHOR

Paolo Dominici (pl.dm(AT)libero.it), May 23 2000

STATUS

approved

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Last modified May 17 14:19 EDT 2022. Contains 353746 sequences. (Running on oeis4.)