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A157993 Number of n-colorings of the Coxeter graph. 2
0, 0, 0, 786240, 397543795824, 3153491495915040, 2897591335142535360, 709217913680036905200, 70921407068068519599840, 3718329027062088400988544, 119720148366778311215868480, 2633253678249157711210367520, 42653023518489941374251310800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The Coxeter Graph is a nonhamiltonian cubic symmetric graph and has 28 vertices and 42 edges.

All terms are multiples of 336.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Timme, Marc; van Bussel, Frank; Fliegner, Denny; Stolzenberg, Sebastian (2009) "Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions", New J. Phys. 11 023001, doi: 10.1088/1367-2630/11/2/023001.

Eric Weisstein's World of Mathematics, Chromatic Polynomial

Eric Weisstein's World of Mathematics, Coxeter Graph

Index entries for linear recurrences with constant coefficients, order 29.

FORMULA

a(n) = n^28 -42*n^27 + ... (see Maple program).

MAPLE

a:= n-> n^28 -42*n^27 +861*n^26 -11480*n^25 +111930*n^24 -850668*n^23 +5245762*n^22 -26977443*n^21 +118014274*n^20 -445705967*n^19 +1469857872*n^18 -4270042980*n^17 +11001634164*n^16 -25266720456*n^15 +51908523754*n^14 -95589692821*n^13 +157862673577*n^12 -233517066853*n^11 +308423840605*n^10 -361701500512*n^9 +373419294214*n^8 -335133871598*n^7 +256750369239*n^6 -163506050813*n^5 +83144968151*n^4 -31635019987*n^3 +7989854148*n^2 -1000876932*n:

seq(a(n), n=0..30);

MATHEMATICA

With[{poly = ChromaticPolynomial[GraphData["CoxeterGraph"]]}, Array[poly, 20]] (* Eric W. Weisstein, May 04 2022 *)

CROSSREFS

Sequence in context: A206633 A184213 A205261 * A175747 A115175 A104949

Adjacent sequences:  A157990 A157991 A157992 * A157994 A157995 A157996

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Mar 10 2009

STATUS

approved

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Last modified July 1 03:30 EDT 2022. Contains 354947 sequences. (Running on oeis4.)