A173705 Number of n-colorings of the 26-Fullerene Graph.

0, 0, 0, 175392, 52636048080, 236901615304560, 136750498496102880, 22791207032346814320, 1646492374456377504672, 65181439861421995954080, 1639402077308605107361920, 28932563258378720821964160, 384247128673776043122297840, 4041651944711085007033425552

Offset: 0

Author

Alois P. Heinz, Nov 25 2010

Keywords

• nonn
• easy

Comments

The 26-Fullerene Graph has 26 nodes and 39 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.
• Eric Weisstein's World of Mathematics, Fullerene
• Wikipedia, Fullerene
• Index entries for linear recurrences with constant coefficients, signature (27, -351, 2925, -17550, 80730, -296010, 888030, -2220075, 4686825, -8436285, 13037895, -17383860, 20058300, -20058300, 17383860, -13037895, 8436285, -4686825, 2220075, -888030, 296010, -80730, 17550, -2925, 351, -27, 1).

Crossrefs

Cf. A173710.

Programs

Maple

a:= n-> n^26 -39*n^25 +741*n^24 -9139*n^23 +82239*n^22 -575334*n^21 +3255381*n^20 -15300714*n^19 [phone]*n^18 -207882246*n^17 [phone]*n^16 -1591600225*n^15 [phone]*n^14 -7231312797*n^13 [phone]*n^12 -19910338640*n^11 [phone]*n^10 -32995251679*n^9 [phone]*n^8 -31516729541*n^7 [phone]*n^6 -15545301211*n^5 [phone]*n^4 -3025373407*n^3 [phone]*n^2 -96255468*n: seq(a(n), n=0..15);

Formula

a(n) = n^26 -39*n^25 + ... (see Maple program).