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

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

Offset: 0

Author

Alois P. Heinz, Dec 04 2013

Keywords

• nonn
• easy

Comments

Also number of n-colorings of the cuboctahedral graph.

Links

• 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).

Crossrefs

Cf. A115400, A140986.

Programs

Maple

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);

Formula

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.