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%I #12 Jan 21 2024 10:21:30
%S 0,0,0,0,342675456,13153078605120,25637821631078400,
%T 9533380086713683200,1227485144606805073920,75547606881603808336896,
%U 2700027498853281914634240,63595142713108801675900800,1076856076493029796330188800,13952190527320266709190514240
%N Number of n-edge-colorings of the second Blanusa Snark.
%C The second Blanusa Snark is a cubic graph on 18 vertices and 27 edges with edge chromatic number 4.
%H Alois P. Heinz, <a href="/A159448/b159448.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/BlanusaSnarks.html">Blanusa Snarks</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EdgeColoring.html">Edge Coloring</a>
%H <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (28, -378, 3276, -20475, 98280, -376740, 1184040, -3108105, 6906900, -13123110, 21474180, -30421755, 37442160, -40116600, 37442160, -30421755, 21474180, -13123110, 6906900, -3108105, 1184040, -376740, 98280, -20475, 3276, -378, 28, -1).
%F a(n) = n^27 -54*n^26 + ... (see Maple program).
%p a:= n-> n^27 -54*n^26 +1413*n^25 -23868*n^24 +292526*n^23 -2771853*n^22 +21128307*n^21 -133083282*n^20 +706103282*n^19 -3200482928*n^18 +12523602732*n^17 -42639446348*n^16 +127040507554*n^15 -332524010611*n^14 +766396617378*n^13 -1556509608394*n^12 +2783042514579*n^11 -4368658864218*n^10 +5990173216956*n^9 -7117375900060*n^8 +7240708340968*n^7 -6196441690112*n^6 +4345188866816*n^5 -2398700714304*n^4 +976694192256*n^3 -260203292160*n^2 +33894503424*n: seq(a(n), n=0..16);
%Y Cf. A159300.
%K nonn
%O 0,5
%A _Alois P. Heinz_, Apr 11 2009
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