A173710 -id:A173710 - cp's OEIS frontend

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

Alois P. Heinz, Nov 25 2010

The 26-Fullerene Graph has 26 nodes and 39 edges.

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).

Cf. A173710.

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 +60877534*n^18 -207882246*n^17 +615460527*n^16 -1591600225*n^15 +3614170438*n^14 -7231312797*n^13 +12771014024*n^12 -19910338640*n^11 +27355291779*n^10 -32995251679*n^9 +34709871301*n^8 -31516729541*n^7 +24310852305*n^6 -15545301211*n^5 +7928693334*n^4 -3025373407*n^3 +766360836*n^2 -96255468*n: seq(a(n), n=0..15);

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

A159191 Number of n-colorings of the Robertson graph.

Original entry on oeis.org

0, 0, 0, 24, 3490848, 3501104400, 564523119840, 31643453033640, 886834653776064, 15220684846368288, 181298924180884800, 1627952400490177080, 11672280987833510880, 69664869701930893104, 357038627052783076128, 1609181428647593728200, 6498071673405936462720

Offset: 0

Alois P. Heinz, Apr 05 2009

The Robertson graph is the unique (4,5) cage: the quartic graph on 19 vertices (so 38 edges) with girth 5.

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. "Robertson Graph".
Weisstein, Eric W. "Chromatic Polynomial".
Index entries for linear recurrences with constant coefficients, signature (20, -190, 1140, -4845, 15504, -38760, 77520, -125970, 167960, -184756, 167960, -125970, 77520, -38760, 15504, -4845, 1140, -190, 20, -1).

The adjacency lists of the Robertson graph are included in A184945.

Cf. A115400, A140986, A157959, A157991, A157992, A157993, A158343, A158344, A158346, A158347, A158348, A158726, A158760, A158792, A158904, A159042, A159055, A159056, A159192, A159299, A166964, A173705, A173710.

a:= n-> n^19 -38*n^18 +703*n^17 -8436*n^16 +73761*n^15 -500004*n^14 +2727105*n^13 -12246808*n^12 +45913333*n^11 -144701057*n^10 +383839223*n^9 -853388854*n^8 +1574465385*n^7 -2370057775*n^6 +2835163369*n^5 -2587310804*n^4 +1685281636*n^3 -693467820*n^2 +134217080*n:
seq(a(n), n=0..20);

a(n) = n^19 -38*n^18 + ... (see Maple program).

cp's OEIS Frontend

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

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