A159191 Number of n-colorings of the Robertson graph.

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

Offset

0,4

Comments

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

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. "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).

Formula

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

Maple

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);

Crossrefs

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.

Sequence in context: A362565 A268505 A172734 * A013820 A294326 A255322

Adjacent sequences: A159188 A159189 A159190 * A159192 A159193 A159194

Keyword

nonn,easy

Author

Alois P. Heinz, Apr 05 2009

Status

approved