A159192 Number of n-colorings of the Brinkmann graph.

0, 0, 0, 0, 17788848, 36105677160, 9840227891760, 838876379282760, 33316659511111200, 770358326829901488, 11901952345453621920, 134595078267062009520, 1187095862662143754320, 8549491024060638451800, 52035271347355128360528, 274779269587463677316280

Offset: 0

Author

Alois P. Heinz, Apr 05 2009

Keywords

• nonn
• easy

Comments

The Brinkmann graph is a quartic graph on 21 vertices and 42 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. "Brinkmann Graph".
• Weisstein, Eric W. "Chromatic Polynomial".
• Index entries for linear recurrences with constant coefficients, signature (22, -231, 1540, -7315, 26334, -74613, 170544, -319770, 497420, -646646, 705432, -646646, 497420, -319770, 170544, -74613, 26334, -7315, 1540, -231, 22, -1).

Programs

Maple

a:= n-> n^21 -42*n^20 +861*n^19 -11480*n^18 +111881*n^17 -848708*n^16 +5207711*n^15 -26500254*n^14 [phone]*n^13 -415278052*n^12 [phone]*n^11 -3483798283*n^10 [phone]*n^9 -15547364853*n^8 [phone]*n^7 -34133692383*n^6 [phone]*n^5 -30480167403*n^4 [phone]*n^3 -6896700738*n^2 [phone]*n: seq(a(n), n=0..20);

Formula

a(n) = n^21 -42*n^20 + ... (see Maple program).