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A309315 Number of 5-colorings of an n-wheel graph. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A334382 A337098 A252953 * A275339 A049058 A056501

Adjacent sequences:  A309312 A309313 A309314 * A309316 A309317 A309318

KEYWORD

nonn,easy

AUTHOR

Aalok Sathe, Jul 23 2019

STATUS

approved

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Last modified April 17 18:15 EDT 2021. Contains 343070 sequences. (Running on oeis4.)