login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A157993
Number of n-colorings of the Coxeter graph.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Mar 10 2009
STATUS
approved