A158347 Number of n-colorings of the Walther Graph.

0, 0, 2, 4033920, 159894687204, 301280127057920, 100770286250343750, 11334165274707633792, 603801344040208577480, 18674487128527060598784, 382076301190534627489290, 5650667805968496542000000, 64331764646611255469788332, 590498122988857695000330240

Offset: 0

Author

Alois P. Heinz, Mar 16 2009

Keywords

• nonn
• easy

Comments

The Walther Graph has 25 vertices and 31 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. "Walther Graph".
• Weisstein, Eric W. "Chromatic Polynomial".
• Index entries for linear recurrences with constant coefficients, signature (26, -325, 2600, -14950, 65780, -230230, 657800, -1562275, 3124550, -5311735, 7726160, -9657700, 10400600, -9657700, 7726160, -5311735, 3124550, -1562275, 657800, -230230, 65780, -14950, 2600, -325, 26, -1).

Programs

Maple

a:= n-> n^25 -31*n^24 +465*n^23 -4494*n^22 +31437*n^21 -169528*n^20 +732875*n^19 -2607473*n^18 +7777403*n^17 -19708162*n^16 [phone]*n^15 -80400727*n^14 [phone]*n^13 -185209067*n^12 [phone]*n^11 -243267982*n^10 [phone]*n^9 -177255496*n^8 [phone]*n^7 -65961560*n^6 [phone]*n^5 -10386912*n^4 +2643810*n^3 -434456*n^2 +34489*n:
seq(a(n), n=0..20);

Formula

a(n) = n^25 -31*n^24 + ... (see Maple program).