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A157991 Number of n-colorings of the Levi Graph.

%I A157991 #14 Feb 16 2025 08:33:09
%S A157991 0,0,2,5514234,2883040542828,40804091270010980,60520556880158419470,
%T A157991 21901769993996949991662,3041658168762971457654584,
%U A157991 211558602330274827202235208,8728129703136293355833601210,239394223814453881755898003490,4731013227415233819791988908772
%N A157991 Number of n-colorings of the Levi Graph.
%C A157991 The Levi Graph has 30 nodes and 45 edges.
%H A157991 Alois P. Heinz, <a href="/A157991/b157991.txt">Table of n, a(n) for n = 0..1000</a>
%H A157991 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 A157991 Weisstein, Eric W. "<a href="https://mathworld.wolfram.com/LeviGraph.html">Levi Graph</a>".
%H A157991 Weisstein, Eric W. "<a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>".
%H A157991 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (31, -465, 4495, -31465, 169911, -736281, 2629575, -7888725, 20160075, -44352165, 84672315, -141120525, 206253075, -265182525, 300540195, -300540195, 265182525, -206253075, 141120525, -84672315, 44352165, -20160075, 7888725, -2629575, 736281, -169911, 31465, -4495, 465, -31, 1).
%F A157991 a(n) = n^30 -45*n^29 + ... (see Maple program).
%p A157991 a:= n-> n^30 -45*n^29 +990*n^28 -14190*n^27 +148995*n^26 -1221759*n^25 +8145060*n^24 -45379530*n^23 +215549775*n^22 -886099793*n^21 +3189425574*n^20 -10143911580*n^19 +28714411485*n^18 -72754429695*n^17 +165716335841*n^16 -340379666835*n^15 +631649660595*n^14 -1059695941005*n^13 +1606062587021*n^12 -2193946401123*n^11 +2690139367971*n^10 -2941870019235*n^9 +2842645627185*n^8 -2395149923590*n^7 +1727156333706*n^6 -1037572912125*n^5 +498710054365*n^4 -179700698265*n^3 +43072277935*n^2 -5133307729*n:
%p A157991 seq(a(n), n=0..30);
%K A157991 nonn,easy
%O A157991 0,3
%A A157991 _Alois P. Heinz_, Mar 10 2009