A158760 Number of n-colorings of the Thomassen graph.

0, 0, 0, 5536512, 76926799438272, 4947985363559224320, 21185449012918739004480, 17588349640445378535417600, 4849123358766202499156608512, 605387426372691102682124470272, 41606924894905120299385749469440, 1794621725353250128205146645205760

Offset: 0

Author

Alois P. Heinz, Mar 25 2009

Keywords

• nonn
• easy

Comments

The Thomassen graph has 34 vertices and 52 edges.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• 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: 10.1088/1367-2630/11/2/023001.
• Weisstein, Eric W. "Thomassen Graphs".
• Weisstein, Eric W. "Chromatic Polynomial".
• Index entries for linear recurrences with constant coefficients, 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).

Programs

Maple

a:= n-> n^34 -52*n^33 +1326*n^32 -22100*n^31 +270701*n^30 -2597792*n^29 [phone]*n^28 -133353844*n^27 [phone]*n^26 -3635709368*n^25 [phone]*n^24 -58521176374*n^23 [phone]*n^22 -592127714794*n^21 [phone]*n^20 -3910652059854*n^19 [phone]*n^18 -17210822423146*n^17 [phone]*n^16 -50848869478506*n^15 [phone]*n^14 -100363167741378*n^13 [phone]*n^12 -129934158329858*n^11 [phone]*n^10 -106418782059034*n^9 [phone]*n^8 -51660687794732*n^7 [phone]*n^6 -13141814264292*n^5 [phone]*n^4 -1337585795996*n^3 [phone]*n^2 -22900610016*n:
seq(a(n), n=0..15);

Formula

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