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A158344 Number of n-colorings of the Folkman Graph.

%I A158344 #20 Feb 16 2025 08:33:09
%S A158344 0,0,2,18648,45718044,22839203000,3322954977390,196998967990272,
%T A158344 6100155102337688,116724860607772944,1546577491554833850,
%U A158344 15357702814950199880,120959689823708363892,787872289121987384328,4380104959751908990694,21297248362250478298800
%N A158344 Number of n-colorings of the Folkman Graph.
%C A158344 The Folkman Graph has 20 vertices and 40 edges. It is the semi-symmetric graph with the fewest possible vertices.
%H A158344 Alois P. Heinz, <a href="/A158344/b158344.txt">Table of n, a(n) for n = 0..1000</a>
%H A158344 Folkman, Jon, <a href="http://www.sciencedirect.com/science/article/pii/S0021980067800693">Regular line-symmetric graphs</a>, Journal of Combinatorial Theory, 3 (3) (1967), 215-232.
%H A158344 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 A158344 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FolkmanGraph.html">Folkman Graph</a>
%H A158344 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>
%H A158344 Wikipedia, <a href="https://en.wikipedia.org/wiki/Folkman_graph">Folkman graph</a>
%H A158344 <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).
%F A158344 a(n) = n^20 -40*n^19 + ... (see Maple program).
%p A158344 a:= n-> n^20 -40*n^19 +780*n^18 -9850*n^17 +90300*n^16 -638683*n^15 +3616080*n^14 -16782060*n^13 +64834630*n^12 -210500726*n^11 +577081604*n^10 -1336290915*n^9 +2602586625*n^8 -4222943355*n^7 +5616671680*n^6 -5968728608*n^5 +4868919865*n^4 -2855170950*n^3 +1066503307*n^2 -189239685*n:
%p A158344 seq(a(n), n=0..30);
%K A158344 nonn,easy
%O A158344 0,3
%A A158344 _Alois P. Heinz_, Mar 16 2009