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A233148 Number of n-edge-colorings of the cubical graph.

%I A233148 #16 Feb 16 2025 08:33:20
%S A233148 0,0,0,24,9216,772680,20864640,281690640,2408469504,14923820016,
%T A233148 72840764160,295839890280,1038542714880,3238606068984,9155710252416,
%U A233148 23832538897440,57817164625920,131989025850720,285757100158464,590483650831416,1170770734955520
%N A233148 Number of n-edge-colorings of the cubical graph.
%C A233148 Also number of n-colorings of the cuboctahedral graph.
%H A233148 Alois P. Heinz, <a href="/A233148/b233148.txt">Table of n, a(n) for n = 0..1000</a>
%H A233148 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicalGraph.html">Cubical Graph</a>
%H A233148 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CuboctahedralGraph.html">Cuboctahedral Graph</a>
%H A233148 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic Polynomial</a>
%H A233148 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).
%F A233148 a(n) = n*(n-1)*(n-2)*(n^9 -21*n^8 +203*n^7 -1191*n^6 +4701*n^5 -13031*n^4 +25524*n^3 -34192*n^2 +28400*n -11072).
%F A233148 G.f.: -24*x^3*(29584*x^9 +491264*x^8 +2823089*x^7 +6622739*x^6 +6646049*x^5 +2837531*x^4 +480491*x^3 +27281*x^2 +371*x+ 1) / (x-1)^13.
%p A233148 a:= n-> n*(n-1)*(n-2) *(-11072 +(28400 +(-34192 +(25524 +(-13031
%p A233148         +(4701 +(-1191 +(203 +(-21+n)*n)*n)*n)*n)*n)*n)*n)*n):
%p A233148 seq(a(n), n=0..30);
%Y A233148 Cf. A115400, A140986.
%K A233148 nonn,easy
%O A233148 0,4
%A A233148 _Alois P. Heinz_, Dec 04 2013