A157993 Number of n-colorings of the Coxeter graph.

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

Offset: 0

Author

Alois P. Heinz, Mar 10 2009

Keywords

• nonn
• easy

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).

Programs

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 [phone]*n^20 -445705967*n^19 [phone]*n^18 -4270042980*n^17 [phone]*n^16 -25266720456*n^15 [phone]*n^14 -95589692821*n^13 [phone]*n^12 -233517066853*n^11 [phone]*n^10 -361701500512*n^9 [phone]*n^8 -335133871598*n^7 [phone]*n^6 -163506050813*n^5 [phone]*n^4 -31635019987*n^3 [phone]*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 *)

Formula

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