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 A094555 Number of walks of length n between two vertices on the same triangular face of a truncated tetrahedron (triangular prism). 7
 0, 1, 1, 6, 11, 46, 111, 386, 1051, 3366, 9671, 29866, 87891, 267086, 794431, 2396946, 7163531, 21545206, 64526391, 193797626, 580955971, 1743741726, 5229477551, 15691927906, 47068793211, 141220360646, 423633119911, 1270955283786 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Average of binomial and inverse binomial transforms of the Jacobsthal numbers A001045. - Paul Barry, Jan 04 2005 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1000 R. J. Mathar, Counting Walks on Finite Graphs, Nov 2020, Section 3. Index entries for linear recurrences with constant coefficients, signature (2,5,-6). FORMULA G.f.: x*(1 - x - x^2)/((1 - x)*(1 + 2*x)*(1 - 3*x)). a(n) = 3^n/6 - (-2)^n/6 + 1/6 - 0^n/6. a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3) for n >= 4. a(n) = Sum_{k=0..floor(n/2)} binomial(n, 2k)*A001045(n-2k). - Paul Barry, Jan 04 2005 E.g.f.: exp(-2*x)*(exp(5*x) + exp(3*x) - exp(2*x) - 1)/6. - Stefano Spezia, Dec 26 2021 MATHEMATICA LinearRecurrence[{2, 5, -6}, {0, 1, 1, 6}, 30] (* Greg Dresden, Jun 19 2021 *) PROG (PARI) a(n) = if(n==0, 0, (3^n - (-2)^n + 1)/6) \\ Andrew Howroyd, Jun 15 2021 CROSSREFS Cf. A001045, A094554, A094556. Sequence in context: A270727 A216269 A242488 * A271056 A271255 A219878 Adjacent sequences: A094552 A094553 A094554 * A094556 A094557 A094558 KEYWORD easy,nonn AUTHOR Paul Barry, May 11 2004 STATUS approved

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Last modified February 22 16:01 EST 2024. Contains 370256 sequences. (Running on oeis4.)