A157992 Number of n-colorings of the Dyck Graph.

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

Offset

0,3

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).

Formula

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

Maple

a:= n-> n^32 -48*n^31 +1128*n^30 -17296*n^29 +194580*n^28 -1712288*n^27 +12270824*n^26 -73614612*n^25 +377151046*n^24 -1675122096*n^23 +6525181008*n^22 -22496343408*n^21 +69142793916*n^20 -190544188160*n^19 +472961919106*n^18 -1061083039384*n^17 +2157059631081*n^16
-3979825893416*n^15 +6668841887020*n^14 -10145667663516*n^13 +13993265083448*n^12 -17447849898820*n^11 +19579417254232*n^10 -19643437430604*n^9 +17454210580012*n^8 -13554627923192*n^7 +9029110616240*n^6 -5021752293076*n^5 +2239517417991*n^4 -750356179848*n^3 +167614890262*n^2 -18665552131*n:
seq(a(n), n=0..30);

Crossrefs

Sequence in context: A170997 A326615 A259407 * A322145 A301810 A296627

Adjacent sequences: A157989 A157990 A157991 * A157993 A157994 A157995

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 10 2009

Status

approved