A157992 Number of n-colorings of the Dyck Graph.

0, 0, 2, 15915138, 20127046304340, 528133663294428020, 1266096501642919005750, 677034005092723101211542, 130523162841884328808537448, 12040770257335491821696076840, 636442821346312893265045966890, 21766425371195465558485996323050

Offset: 0

Author

Alois P. Heinz, Mar 10 2009

Keywords

• nonn
• easy

Comments

The Dyck Graph has 32 nodes and 48 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. "Dyck Graph".
• Weisstein, Eric W. "Chromatic Polynomial".
• Index entries for linear recurrences with constant coefficients, signature (33, -528, 5456, -40920, 237336, -1107568, 4272048, -13884156, 38567100, -92561040, 193536720, -354817320, 573166440, -818809200, 1037158320, -1166803110, 1166803110, -1037158320, 818809200, -573166440, 354817320, -193536720, 92561040, -38567100, 13884156, -4272048, 1107568, -237336, 40920, -5456, 528, -33, 1).

Programs

Maple

a:= n-> n^32 -48*n^31 +1128*n^30 -17296*n^29 +194580*n^28 -1712288*n^27 [phone]*n^26 -73614612*n^25 [phone]*n^24 -1675122096*n^23 [phone]*n^22 -22496343408*n^21 [phone]*n^20 -190544188160*n^19 [phone]*n^18 -1061083039384*n^17 [phone]*n^16
-3979825893416*n^15 [phone]*n^14 -10145667663516*n^13 [phone]*n^12 -17447849898820*n^11 [phone]*n^10 -19643437430604*n^9 [phone]*n^8 -13554627923192*n^7 [phone]*n^6 -5021752293076*n^5 [phone]*n^4 -750356179848*n^3 [phone]*n^2 -18665552131*n:
seq(a(n), n=0..30);

Formula

a(n) = n^32 -48*n^31 + ... (see Maple program).