A165216 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994908, 1207958976, 9663669540, 77309338176, 618474560256, 4947795320832, 39582353276928, 316658751897600, 2533269420638208, 20266150608766188, 162129166819422768

Offset: 0

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Keywords

• nonn

Comments

The initial terms coincide with those of A003951, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

• Index entries for linear recurrences with constant coefficients, signature (7, 7, 7, 7, 7, 7, 7, 7, -28).

Programs

Mathematica

With[{num=Total[2t^Range[8]]+t^9+1,den=Total[-7 t^Range[8]]+ 28t^9+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Oct 02 2011 *)

Formula

G.f. (t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +

1)/(28*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t

+ 1)