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A159192 Number of n-colorings of the Brinkmann graph.

%I A159192 #15 Feb 16 2025 08:33:10
%S A159192 0,0,0,0,17788848,36105677160,9840227891760,838876379282760,
%T A159192 33316659511111200,770358326829901488,11901952345453621920,
%U A159192 134595078267062009520,1187095862662143754320,8549491024060638451800,52035271347355128360528,274779269587463677316280
%N A159192 Number of n-colorings of the Brinkmann graph.
%C A159192 The Brinkmann graph is a quartic graph on 21 vertices and 42 edges.
%H A159192 Alois P. Heinz, <a href="/A159192/b159192.txt">Table of n, a(n) for n = 0..1000</a>
%H A159192 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 A159192 Weisstein, Eric W. "<a href="https://mathworld.wolfram.com/BrinkmannGraph.html">Brinkmann Graph</a>".
%H A159192 Weisstein, Eric W. "<a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>".
%H A159192 <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (22, -231, 1540, -7315, 26334, -74613, 170544, -319770, 497420, -646646, 705432, -646646, 497420, -319770, 170544, -74613, 26334, -7315, 1540, -231, 22, -1).
%F A159192 a(n) = n^21 -42*n^20 + ... (see Maple program).
%p A159192 a:= n-> n^21 -42*n^20 +861*n^19 -11480*n^18 +111881*n^17 -848708*n^16 +5207711*n^15 -26500254*n^14 +113675219*n^13 -415278052*n^12 +1299042255*n^11 -3483798283*n^10 +7987607279*n^9 -15547364853*n^8 +25384350310*n^7 -34133692383*n^6 +36783818141*n^5 -30480167403*n^4 +18168142566*n^3 -6896700738*n^2 +1242405972*n: seq(a(n), n=0..20);
%K A159192 nonn,easy
%O A159192 0,5
%A A159192 _Alois P. Heinz_, Apr 05 2009