A157959 Number of n-colorings of the Desargues graph.

0, 0, 2, 42258, 217727724, 120716639420, 15509657482350, 784759781145102, 21017383336908728, 355260899699333784, 4240584584018848890, 38562180170120230250, 281853103175962977252, 1722023964356731913748, 9058240485370625897894, 41970560739174197375910

Offset: 0

Author

Alois P. Heinz, Mar 10 2009

Keywords

• nonn
• easy

Comments

The Desargues graph is a cubic symmetric distance-regular graph with 20 vertices and 30 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.
• Eric Weisstein's World of Mathematics, "Desargues Graph".
• Eric Weisstein's World of Mathematics, "Chromatic Polynomial".
• Index entries for linear recurrences with constant coefficients, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).

Programs

Maple

a:= n-> n^20 -30*n^19 +435*n^18 -4060*n^17 +27405*n^16 -142486*n^15 +593275*n^14 -2029770*n^13 +5806295*n^12 -14047858*n^11 [phone]*n^10 -50912200*n^9 [phone]*n^8 -96864050*n^7 [phone]*n^6 -88808037*n^5 [phone]*n^4 -30272495*n^3 +9922451*n^2 -1585121*n: seq(a(n), n=0..30);

Formula

a(n) = n^20 -30*n^19 +435*n^18 -4060*n^17 +27405*n^16 -142486*n^15 +593275*n^14 -2029770*n^13 +5806295*n^12 -14047858*n^11 [phone]*n^10 -50912200*n^9 [phone]*n^8 -96864050*n^7 [phone]*n^6 -88808037*n^5 [phone]*n^4 -30272495*n^3 +9922451*n^2 -1585121*n.