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

3,1

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).

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)

Prog

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

Crossrefs

Cf. A010677, A090860.

Sequence in context: A337098 A379753 A252953 * A275339 A049058 A056501

Adjacent sequences: A309312 A309313 A309314 * A309316 A309317 A309318

Keyword

nonn,easy,changed

Author

Aalok Sathe, Jul 23 2019

Status

approved