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%I #14 Jan 31 2024 12:07:44
%S 0,0,0,0,28560,18277200,1925512560,71729634480,1389478980960,
%T 17119717947360,151217975815200,1034656343471520,5783087147848560,
%U 27431854405990320,113598910323858960,419654992044834000,1406448998999378880,4333949766504066240,12412819895060854080
%N Number of n-colorings of the Clebsch Graph.
%C The Clebsch Graph or Greenwood-Gleason Graph is a strongly regular quintic graph on 16 vertices and 40 edges.
%H Alois P. Heinz, <a href="/A159056/b159056.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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ClebschGraph.html">Clebsch Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>
%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).
%F a(n) = n^16 -40*n^15 + ... (see Maple program).
%p a:= n-> n^16 -40*n^15 +780*n^14 -9840*n^13 +89718*n^12 -624856*n^11 +3423400*n^10 -14966420*n^9 +52409081*n^8 -146275504*n^7 +320950404*n^6 -540248540*n^5 +670404830*n^4 -573961940*n^3 +299904066*n^2 -71095140*n:
%p seq(a(n), n=0..25);
%K nonn,easy
%O 0,5
%A _Alois P. Heinz_, Apr 03 2009