A159055 Number of n-colorings of the Small Rhombicuboctahedral Graph.

0, 0, 0, 576, 203650128, 1040638993440, 623084813563680, 101592631680840720, 6943164801523811616, 255263918698905355008, 5904362798572834500480, 95380230960557432984160, 1157524686225195065529840, 11126698756531124744948256, 88134022363811246118729888

Offset: 0

Author

Alois P. Heinz, Apr 03 2009

Keywords

• nonn
• easy

Comments

The Small Rhombicuboctahedral Graph is a quartic graph and has 24 vertices and 48 edges.

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. "Small Rhombicuboctahedral Graph".
• Weisstein, Eric W. "Chromatic Polynomial".
• Index entries for linear recurrences with constant coefficients, signature (25, -300, 2300, -12650, 53130, -177100, 480700, -1081575, 2042975, -3268760, 4457400, -5200300, 5200300, -4457400, 3268760, -2042975, 1081575, -480700, 177100, -53130, 12650, -2300, 300, -25, 1).

Programs

Maple

a:= n-> n^24 -48*n^23 +1120*n^22 -16910*n^21 +185518*n^20 -1574420*n^19 [phone]*n^18 -60484598*n^17 [phone]*n^16 -1150897784*n^15 [phone]*n^14 -11858250846*n^13 [phone]*n^12 -68798913942*n^11 [phone]*n^10 -224828818477*n^9 [phone]*n^8 -395626119514*n^7 [phone]*n^6 -332539017926*n^5 [phone]*n^4 -100567383387*n^3 [phone]*n^2 -4486439772*n:
seq(a(n), n=0..20);

Formula

a(n) = n^24 -48*n^23 + ... (see Maple program).