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A158347 Number of n-colorings of the Walther Graph.

%I A158347 #15 Feb 16 2025 08:33:09
%S A158347 0,0,2,4033920,159894687204,301280127057920,100770286250343750,
%T A158347 11334165274707633792,603801344040208577480,18674487128527060598784,
%U A158347 382076301190534627489290,5650667805968496542000000,64331764646611255469788332,590498122988857695000330240
%N A158347 Number of n-colorings of the Walther Graph.
%C A158347 The Walther Graph has 25 vertices and 31 edges.
%H A158347 Alois P. Heinz, <a href="/A158347/b158347.txt">Table of n, a(n) for n = 0..1000</a>
%H A158347 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 A158347 Weisstein, Eric W. "<a href="https://mathworld.wolfram.com/WaltherGraph.html">Walther Graph</a>".
%H A158347 Weisstein, Eric W. "<a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>".
%H A158347 <a href="/index/Rec#order_26">Index entries for linear recurrences with constant coefficients</a>, signature (26, -325, 2600, -14950, 65780, -230230, 657800, -1562275, 3124550, -5311735, 7726160, -9657700, 10400600, -9657700, 7726160, -5311735, 3124550, -1562275, 657800, -230230, 65780, -14950, 2600, -325, 26, -1).
%F A158347 a(n) = n^25 -31*n^24 + ... (see Maple program).
%p A158347 a:= n-> n^25 -31*n^24 +465*n^23 -4494*n^22 +31437*n^21 -169528*n^20 +732875*n^19 -2607473*n^18 +7777403*n^17 -19708162*n^16 +42836515*n^15 -80400727*n^14 +130882589*n^13 -185209067*n^12 +227870356*n^11 -243267982*n^10 +224314530*n^9 -177255496*n^8 +118586759*n^7 -65961560*n^6 +29694659*n^5 -10386912*n^4 +2643810*n^3 -434456*n^2 +34489*n:
%p A158347 seq(a(n), n=0..20);
%K A158347 nonn,easy
%O A158347 0,3
%A A158347 _Alois P. Heinz_, Mar 16 2009