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A159191 Number of n-colorings of the Robertson graph. 2
0, 0, 0, 24, 3490848, 3501104400, 564523119840, 31643453033640, 886834653776064, 15220684846368288, 181298924180884800, 1627952400490177080, 11672280987833510880, 69664869701930893104, 357038627052783076128, 1609181428647593728200, 6498071673405936462720 (list; graph; refs; listen; history; text; internal format)
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

Weisstein, Eric W. "Robertson Graph".

Weisstein, Eric W. "Chromatic Polynomial".

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.

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, A158760, A158792, A158904, A159042, A159055, A159056, A159192, A159299, A166964, A173705, A173710.

Sequence in context: A319977 A268505 A172734 * A013820 A294326 A255322

Adjacent sequences:  A159188 A159189 A159190 * A159192 A159193 A159194

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 05 2009

STATUS

approved

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Last modified December 2 22:46 EST 2021. Contains 349445 sequences. (Running on oeis4.)