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A054881 Number of walks of length n along the edges of an octahedron starting and ending at a vertex and also ( with a(0)=0 ) between two opposite vertices. 7
1, 0, 4, 8, 48, 160, 704, 2688, 11008, 43520, 175104, 698368, 2797568, 11182080, 44744704, 178946048, 715849728, 2863267840, 11453333504, 45812809728, 183252287488, 733007052800, 2932032405504, 11728121233408 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

R. J. Mathar, Counting Walks on Finite Graphs, Nov 2020, Section 7.

Index entries for linear recurrences with constant coefficients, signature (2,8).

FORMULA

a(n+1)/4 = A003683(n), n >= 0.

a(n) = (4^n+(-1)^n*2^(n+1))/6 for n>0.

G.f.: 1/2+1/3/(1+2*x)+1/6/(1-4*x).

G.f.: (1-2*x-4*x^2)/((1+2*x)*(1-4*x)). - L. Edson Jeffery, Apr 22 2015

a(n+3) = 8*A246036(n), n >= 0. - L. Edson Jeffery, Apr 22 2015

a(n+1) = 2^(n+1)*A001045(n) = 2^(n+1)*(2^n - (-1)^n)/3, n >= 0. - Ralf Steiner, Aug 27 2020, edited by M. F. Hasler, Sep 11 2020

MATHEMATICA

CoefficientList[Series[(1 - 2*x - 4*x^2)/((1 + 2 x)*(1 - 4 x)), {x, 0, 23}], x] (* L. Edson Jeffery, Apr 22 2015 *)

PROG

(Magma) [1] cat [(4^n+(-1)^n*2^(n+1))/6: n in [1..30]]; // Vincenzo Librandi, Apr 23 2015

CROSSREFS

Cf. A003683, A246036.

Sequence in context: A087261 A249572 A078236 * A045882 A051681 A267987

Adjacent sequences: A054878 A054879 A054880 * A054882 A054883 A054884

KEYWORD

nonn,walk,easy

AUTHOR

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

STATUS

approved

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)