The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A328778 Number of indecomposable closed walks of length 2n along the edges of a cube based at a vertex. 4
 1, 3, 12, 84, 588, 4116, 28812, 201684, 1411788, 9882516, 69177612, 484243284, 3389702988, 23727920916, 166095446412, 1162668124884, 8138676874188, 56970738119316, 398795166835212, 2791566167846484, 19540963174925388 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS An indecomposable closed walk returns to its starting vertex exactly once (on the final step). For n > 1, a(n) is the number of 4-colorings of the grid graph P_2 X P_(n-1). More generally, for q > 1, the number of q-colorings of the grid graph P_2 X P_n is given by q*(q - 1)*((q - 1)*(q - 2) + 1)^(n - 1). - Sela Fried, Sep 25 2023 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (7). FORMULA G.f.: 2 - 1/f(x) where f(x) is the g.f. for A054879. From Colin Barker, Oct 27 2019: (Start) G.f.: (1 - 4*x - 9*x^2) / (1 - 7*x). a(n) = 7*a(n-1) for n>2. a(n) = 12*7^(n - 2) for n>1. (End) E.g.f.: (1/49)*(37 + 12*exp(7*x) + 63*x). - Stefano Spezia, Oct 27 2019 MATHEMATICA nn = 40; list = Range[0, nn]! CoefficientList[Series[ Cosh[x]^3, {x, 0, nn}], x]; a = Sum[list[[i]] x^(i - 1), {i, 1, nn + 1}]; Select[CoefficientList[Series[ 2 - 1/a, {x, 0, nn}], x], # > 0 &] PROG (PARI) Vec((1 - 4*x - 9*x^2) / (1 - 7*x) + O(x^25)) \\ Colin Barker, Oct 28 2019 CROSSREFS Cf. A054879, A025192. Sequence in context: A245775 A277782 A066780 * A231868 A147835 A032183 Adjacent sequences: A328775 A328776 A328777 * A328779 A328780 A328781 KEYWORD nonn,walk,easy AUTHOR Geoffrey Critzer, Oct 27 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 5 03:48 EST 2023. Contains 367567 sequences. (Running on oeis4.)