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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. 5
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

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

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

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 * A076687 A045882 A051681

Adjacent sequences:  A054878 A054879 A054880 * A054882 A054883 A054884

KEYWORD

nonn,walk

AUTHOR

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

STATUS

approved

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Last modified April 24 09:21 EDT 2017. Contains 285338 sequences.