A115400 -id:A115400 - cp's OEIS frontend

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

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).

A233148 Number of n-edge-colorings of the cubical graph.

Original entry on oeis.org

0, 0, 0, 24, 9216, 772680, 20864640, 281690640, 2408469504, 14923820016, 72840764160, 295839890280, 1038542714880, 3238606068984, 9155710252416, 23832538897440, 57817164625920, 131989025850720, 285757100158464, 590483650831416, 1170770734955520

Offset: 0

Alois P. Heinz, Dec 04 2013

Also number of n-colorings of the cuboctahedral graph.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Cubical Graph
Eric Weisstein's World of Mathematics, Cuboctahedral Graph
Wikipedia, Chromatic Polynomial
Index entries for linear recurrences with constant coefficients, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).

Cf. A115400, A140986.

a:= n-> n*(n-1)*(n-2) *(-11072 +(28400 +(-34192 +(25524 +(-13031
        +(4701 +(-1191 +(203 +(-21+n)*n)*n)*n)*n)*n)*n)*n)*n):
seq(a(n), n=0..30);

a(n) = n*(n-1)*(n-2)*(n^9 -21*n^8 +203*n^7 -1191*n^6 +4701*n^5 -13031*n^4 +25524*n^3 -34192*n^2 +28400*n -11072).

G.f.: -24*x^3*(29584*x^9 +491264*x^8 +2823089*x^7 +6622739*x^6 +6646049*x^5 +2837531*x^4 +480491*x^3 +27281*x^2 +371*x+ 1) / (x-1)^13.

cp's OEIS Frontend

A159191 Number of n-colorings of the Robertson graph.

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