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A094556 Number of walks of length n between opposite vertices on a triangular prism. 4
0, 1, 0, 7, 8, 51, 100, 407, 1008, 3451, 9500, 30207, 87208, 268451, 791700, 2402407, 7152608, 21567051, 64482700, 193885007, 580781208, 1744091251, 5228778500, 15693326007, 47065997008, 141225953051, 423621935100, 1270977653407 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
R. J. Mathar, Counting Walks on Finite Graphs, Nov 2020, Section 3.
FORMULA
G.f.: x*(1 - 2*x + 2*x^2)/((1 - x)*(1 + 2*x)*(1 - 3*x)).
a(n) = 3^n/6 - (-2)^n/3 - 1/6 + 0^n/3.
a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3) for n >= 4.
E.g.f.: exp(-x)*(2+exp(3*x))*sinh(x)/3. - Stefano Spezia, Sep 26 2023
MATHEMATICA
LinearRecurrence[{2, 5, -6}, {0, 1, 0, 7}, 30] (* or *) CoefficientList[ Series[ x (1-2x+2x^2)/((1-x)(1+2x)(1-3x)), {x, 0, 30}], x] (* Harvey P. Dale, Jul 13 2011 *)
PROG
(PARI) a(n) = if(n==0, 0, (3^n - 2*(-2)^n - 1)/6) \\ Andrew Howroyd, Jun 15 2021
CROSSREFS
Sequence in context: A038274 A201919 A249310 * A249329 A041023 A041108
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 11 2004
STATUS
approved

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Last modified February 24 07:07 EST 2024. Contains 370294 sequences. (Running on oeis4.)