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Number of n-colorings of the Small Rhombicuboctahedral Graph.
2

%I #14 Jan 31 2024 12:07:17

%S 0,0,0,576,203650128,1040638993440,623084813563680,101592631680840720,

%T 6943164801523811616,255263918698905355008,5904362798572834500480,

%U 95380230960557432984160,1157524686225195065529840,11126698756531124744948256,88134022363811246118729888

%N Number of n-colorings of the Small Rhombicuboctahedral Graph.

%C The Small Rhombicuboctahedral Graph is a quartic graph and has 24 vertices and 48 edges.

%H Alois P. Heinz, <a href="/A159055/b159055.txt">Table of n, a(n) for n = 0..1000</a>

%H 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 Weisstein, Eric W. "<a href="http://mathworld.wolfram.com/SmallRhombicuboctahedralGraph.html">Small Rhombicuboctahedral Graph</a>".

%H Weisstein, Eric W. "<a href="http://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>".

%H <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (25, -300, 2300, -12650, 53130, -177100, 480700, -1081575, 2042975, -3268760, 4457400, -5200300, 5200300, -4457400, 3268760, -2042975, 1081575, -480700, 177100, -53130, 12650, -2300, 300, -25, 1).

%F a(n) = n^24 -48*n^23 + ... (see Maple program).

%p a:= n-> n^24 -48*n^23 +1120*n^22 -16910*n^21 +185518*n^20 -1574420*n^19 +10743365*n^18 -60484598*n^17 +286043853*n^16 -1150897784*n^15 +3975180762*n^14 -11858250846*n^13 +30660467874*n^12 -68798913942*n^11 +133829611744*n^10 -224828818477*n^9 +323901249982*n^8 -395626119514*n^7 +402626826190*n^6 -332539017926*n^5 +214063824663*n^4 -100567383387*n^3 +30563782552*n^2 -4486439772*n:

%p seq(a(n), n=0..20);

%K nonn,easy

%O 0,4

%A _Alois P. Heinz_, Apr 03 2009