cp's OEIS Frontend

A309315 Number of 5-colorings of an n-wheel graph.

%I A309315 #32 Feb 16 2025 08:33:55
%S A309315 60,120,420,1200,3660,10920,32820,98400,295260,885720,2657220,7971600,
%T A309315 23914860,71744520,215233620,645700800,1937102460,5811307320,
%U A309315 17433922020,52301766000,156905298060,470715894120,1412147682420,4236443047200,12709329141660
%N A309315 Number of 5-colorings of an n-wheel graph.
%C A309315 Cf. A010677 (for 3-colorings), A090860 (for 4-colorings).
%H A309315 Colin Barker, <a href="/A309315/b309315.txt">Table of n, a(n) for n = 3..1000</a>
%H A309315 Prateek Bhakta, Benjamin Brett Buckner, Lauren Farquhar, Vikram Kamat, Sara Krehbiel, Heather M. Russell, <a href="https://doi.org/10.1007/s00373-018-1985-6">Cut-Colorings in Coloring Graphs</a>, Graphs and Combinatorics, (2019) 35(1), 239-248.
%H A309315 Luis Cereceda, Janvan den Heuvel, Matthew Johnson, <a href="https://doi.org/10.1016/j.disc.2007.07.028">Connectedness of the graph of vertex-colourings</a>, Discrete Mathematics, (2008) 308(5-6), 913-919.
%H A309315 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WheelGraph.html">Wheel Graph</a>
%H A309315 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic polynomial</a>
%H A309315 Wikipedia, <a href="https://en.wikipedia.org/wiki/Wheel_graph">Wheel graph</a>
%H A309315 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,3).
%F A309315 a(n) = 5*3^(n-1)-15*(-1)^n.
%F A309315 From _Colin Barker_, Jul 24 2019: (Start)
%F A309315 G.f.: 60*x^3 / ((1 + x)*(1 - 3*x)).
%F A309315 a(n) = 2*a(n-1) + 3*a(n-2) for n>4.
%F A309315 (End)
%o A309315 (PARI) Vec(60*x^3 / ((1 + x)*(1 - 3*x)) + O(x^30)) \\ _Colin Barker_, Jul 24 2019
%Y A309315 Cf. A010677, A090860.
%K A309315 nonn,easy
%O A309315 3,1
%A A309315 _Aalok Sathe_, Jul 23 2019