

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
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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/(14*x).
G.f.: (12*x4*x^2)/((1+2*x)*(14*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



