A157993 Number of n-colorings of the Coxeter graph.

0, 0, 0, 786240, 397543795824, 3153491495915040, 2897591335142535360, 709217913680036905200, 70921407068068519599840, 3718329027062088400988544, 119720148366778311215868480, 2633253678249157711210367520, 42653023518489941374251310800

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

Marc Timme, Frank van Bussel, Denny Fliegner, and Sebastian Stolzenberg, Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions, New Journal of Physics, Volume 11, February 2009.

Eric Weisstein's World of Mathematics, Chromatic Polynomial

Eric Weisstein's World of Mathematics, Coxeter Graph

Index entries for linear recurrences with constant coefficients, signature (29, -406, 3654, -23751, 118755, -475020, 1560780, -4292145, 10015005, -20030010, 34597290, -51895935, 67863915, -77558760, 77558760, -67863915, 51895935, -34597290, 20030010, -10015005, 4292145, -1560780, 475020, -118755, 23751, -3654, 406, -29, 1).

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 A355707 A115175

Adjacent sequences: A157990 A157991 A157992 * A157994 A157995 A157996

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 10 2009

Status

approved