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

60, 120, 420, 1200, 3660, 10920, 32820, 98400, 295260, 885720, 2657220, 7971600, 23914860, 71744520, 215233620, 645700800, 1937102460, 5811307320, 17433922020, 52301766000, 156905298060, 470715894120, 1412147682420, 4236443047200, 12709329141660

Offset: 3

Author

Aalok Sathe, Jul 23 2019

Keywords

• nonn
• easy

Comments

Cf. A010677 (for 3-colorings), A090860 (for 4-colorings).

Links

• Colin Barker, Table of n, a(n) for n = 3..1000
• Prateek Bhakta, Benjamin Brett Buckner, Lauren Farquhar, Vikram Kamat, Sara Krehbiel, Heather M. Russell, Cut-Colorings in Coloring Graphs, Graphs and Combinatorics, (2019) 35(1), 239-248.
• Luis Cereceda, Janvan den Heuvel, Matthew Johnson, Connectedness of the graph of vertex-colourings, Discrete Mathematics, (2008) 308(5-6), 913-919.
• Eric Weisstein's World of Mathematics, Wheel Graph
• Wikipedia, Chromatic polynomial
• Wikipedia, Wheel graph
• Index entries for linear recurrences with constant coefficients, signature (2,3).

Crossrefs

Cf. A010677, A090860.

Programs

PARI

Vec(60*x^3 / ((1 + x)*(1 - 3*x)) + O(x^30)) \\ Colin Barker, Jul 24 2019

Formula

a(n) = 5*3^(n-1)-15*(-1)^n.

From Colin Barker, Jul 24 2019: (Start)

G.f.: 60*x^3 / ((1 + x)*(1 - 3*x)).

a(n) = 2*a(n-1) + 3*a(n-2) for n>4.

(End)