A159056 Number of n-colorings of the Clebsch Graph.

0, 0, 0, 0, 28560, 18277200, 1925512560, 71729634480, 1389478980960, 17119717947360, 151217975815200, 1034656343471520, 5783087147848560, 27431854405990320, 113598910323858960, 419654992044834000, 1406448998999378880, 4333949766504066240, 12412819895060854080

Offset: 0

Author

Alois P. Heinz, Apr 03 2009

Keywords

• nonn
• easy

Comments

The Clebsch Graph or Greenwood-Gleason Graph is a strongly regular quintic graph on 16 vertices and 40 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, Clebsch Graph
• Eric Weisstein's World of Mathematics, Chromatic Polynomial
• Index entries for linear recurrences with constant coefficients, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).

Programs

Maple

a:= n-> n^16 -40*n^15 +780*n^14 -9840*n^13 +89718*n^12 -624856*n^11 +3423400*n^10 -14966420*n^9 [phone]*n^8 -146275504*n^7 [phone]*n^6 -540248540*n^5 [phone]*n^4 -573961940*n^3 [phone]*n^2 -71095140*n:
seq(a(n), n=0..25);

Formula

a(n) = n^16 -40*n^15 + ... (see Maple program).