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A157959 Number of n-colorings of the Desargues graph.

%I A157959 #17 Feb 16 2025 08:33:09
%S A157959 0,0,2,42258,217727724,120716639420,15509657482350,784759781145102,
%T A157959 21017383336908728,355260899699333784,4240584584018848890,
%U A157959 38562180170120230250,281853103175962977252,1722023964356731913748,9058240485370625897894,41970560739174197375910
%N A157959 Number of n-colorings of the Desargues graph.
%C A157959 The Desargues graph is a cubic symmetric distance-regular graph with 20 vertices and 30 edges.
%H A157959 Alois P. Heinz, <a href="/A157959/b157959.txt">Table of n, a(n) for n = 0..1000</a>
%H A157959 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 A157959 Eric Weisstein's World of Mathematics, "<a href="https://mathworld.wolfram.com/DesarguesGraph.html">Desargues Graph</a>".
%H A157959 Eric Weisstein's World of Mathematics, "<a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>".
%H A157959 <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).
%F A157959 a(n) = n^20 -30*n^19 +435*n^18 -4060*n^17 +27405*n^16 -142486*n^15 +593275*n^14 -2029770*n^13 +5806295*n^12 -14047858*n^11 +28942903*n^10 -50912200*n^9 +76328405*n^8 -96864050*n^7 +102660272*n^6 -88808037*n^5 +60384665*n^4 -30272495*n^3 +9922451*n^2 -1585121*n.
%p A157959 a:= n-> n^20 -30*n^19 +435*n^18 -4060*n^17 +27405*n^16 -142486*n^15 +593275*n^14 -2029770*n^13 +5806295*n^12 -14047858*n^11 +28942903*n^10 -50912200*n^9 +76328405*n^8 -96864050*n^7 +102660272*n^6 -88808037*n^5 +60384665*n^4 -30272495*n^3 +9922451*n^2 -1585121*n: seq(a(n), n=0..30);
%K A157959 nonn,easy
%O A157959 0,3
%A A157959 _Alois P. Heinz_, Mar 10 2009