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A159191 Number of n-colorings of the Robertson graph.

%I A159191 #19 Feb 16 2025 08:33:10
%S A159191 0,0,0,24,3490848,3501104400,564523119840,31643453033640,
%T A159191 886834653776064,15220684846368288,181298924180884800,
%U A159191 1627952400490177080,11672280987833510880,69664869701930893104,357038627052783076128,1609181428647593728200,6498071673405936462720
%N A159191 Number of n-colorings of the Robertson graph.
%C A159191 The Robertson graph is the unique (4,5) cage: the quartic graph on 19 vertices (so 38 edges) with girth 5.
%H A159191 Alois P. Heinz, <a href="/A159191/b159191.txt">Table of n, a(n) for n = 0..1000</a>
%H A159191 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: <a href="http://dx.doi.org/10.1088/1367-2630/11/2/023001">10.1088/1367-2630/11/2/023001</a>.
%H A159191 Weisstein, Eric W. "<a href="https://mathworld.wolfram.com/RobertsonGraph.html">Robertson Graph</a>".
%H A159191 Weisstein, Eric W. "<a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>".
%H A159191 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (20, -190, 1140, -4845, 15504, -38760, 77520, -125970, 167960, -184756, 167960, -125970, 77520, -38760, 15504, -4845, 1140, -190, 20, -1).
%F A159191 a(n) = n^19 -38*n^18 + ... (see Maple program).
%p A159191 a:= n-> n^19 -38*n^18 +703*n^17 -8436*n^16 +73761*n^15 -500004*n^14 +2727105*n^13 -12246808*n^12 +45913333*n^11 -144701057*n^10 +383839223*n^9 -853388854*n^8 +1574465385*n^7 -2370057775*n^6 +2835163369*n^5 -2587310804*n^4 +1685281636*n^3 -693467820*n^2 +134217080*n:
%p A159191 seq(a(n), n=0..20);
%Y A159191 The adjacency lists of the Robertson graph are included in A184945.
%Y A159191 Cf. A115400, A140986, A157959, A157991, A157992, A157993, A158343, A158344, A158346, A158347, A158348, A158726, A158760, A158792, A158904, A159042, A159055, A159056, A159192, A159299, A166964, A173705, A173710.
%K A159191 nonn,easy
%O A159191 0,4
%A A159191 _Alois P. Heinz_, Apr 05 2009