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A158760 Number of n-colorings of the Thomassen graph. 2

%I #14 Jan 31 2024 12:05:47

%S 0,0,0,5536512,76926799438272,4947985363559224320,

%T 21185449012918739004480,17588349640445378535417600,

%U 4849123358766202499156608512,605387426372691102682124470272,41606924894905120299385749469440,1794621725353250128205146645205760

%N Number of n-colorings of the Thomassen graph.

%C The Thomassen graph has 34 vertices and 52 edges.

%H Alois P. Heinz, <a href="/A158760/b158760.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/ThomassenGraphs.html">Thomassen Graphs</a>".

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

%H <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (35, -595, 6545, -52360, 324632, -1623160, 6724520, -23535820, 70607460, -183579396, 417225900, -834451800, 1476337800, -2319959400, 3247943160, -4059928950, 4537567650, -4537567650, 4059928950, -3247943160, 2319959400, -1476337800, 834451800, -417225900, 183579396, -70607460, 23535820, -6724520, 1623160, -324632, 52360, -6545, 595, -35, 1).

%F a(n) = n^34 -52*n^33 + ... (see Maple program).

%p a:= n-> n^34 -52*n^33 +1326*n^32 -22100*n^31 +270701*n^30 -2597792*n^29 +20330732*n^28 -133353844*n^27 +747647506*n^26 -3635709368*n^25 +15507433860*n^24 -58521176374*n^23 +196717789794*n^22 -592127714794*n^21 +1602439699436*n^20 -3910652059854*n^19 +8624512792549*n^18 -17210822423146*n^17 +31094378683270*n^16 -50848869478506*n^15 +75192226394861*n^14 -100363167741378*n^13 +120588516202821*n^12 -129934158329858*n^11 +124914069641504*n^10 -106418782059034*n^9 +79614672879790*n^8 -51660687794732*n^7 +28576510153968*n^6 -13141814264292*n^5 +4836250627461*n^4 -1337585795996*n^3 +247290581556*n^2 -22900610016*n:

%p seq(a(n), n=0..15);

%K nonn,easy

%O 0,4

%A _Alois P. Heinz_, Mar 25 2009

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Last modified April 25 05:56 EDT 2024. Contains 371964 sequences. (Running on oeis4.)