A157991 Number of n-colorings of the Levi Graph.

0, 0, 2, 5514234, 2883040542828, 40804091270010980, 60520556880158419470, 21901769993996949991662, 3041658168762971457654584, 211558602330274827202235208, 8728129703136293355833601210, 239394223814453881755898003490, 4731013227415233819791988908772

Offset: 0

Author

Alois P. Heinz, Mar 10 2009

Keywords

• nonn
• easy

Comments

The Levi Graph has 30 nodes and 45 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. "Levi Graph".
• Weisstein, Eric W. "Chromatic Polynomial".
• Index entries for linear recurrences with constant coefficients, signature (31, -465, 4495, -31465, 169911, -736281, 2629575, -7888725, 20160075, -44352165, 84672315, -141120525, 206253075, -265182525, 300540195, -300540195, 265182525, -206253075, 141120525, -84672315, 44352165, -20160075, 7888725, -2629575, 736281, -169911, 31465, -4495, 465, -31, 1).

Programs

Maple

a:= n-> n^30 -45*n^29 +990*n^28 -14190*n^27 +148995*n^26 -1221759*n^25 +8145060*n^24 -45379530*n^23 [phone]*n^22 -886099793*n^21 [phone]*n^20 -10143911580*n^19 [phone]*n^18 -72754429695*n^17 [phone]*n^16 -340379666835*n^15 [phone]*n^14 -1059695941005*n^13 [phone]*n^12 -2193946401123*n^11 [phone]*n^10 -2941870019235*n^9 [phone]*n^8 -2395149923590*n^7 [phone]*n^6 -1037572912125*n^5 [phone]*n^4 -179700698265*n^3 [phone]*n^2 -5133307729*n:
seq(a(n), n=0..30);

Formula

a(n) = n^30 -45*n^29 + ... (see Maple program).