A165213 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 6, 30, 150, 750, 3750, 18750, 93750, 468750, 2343735, 11718600, 58592640, 292961400, 1464798000, 7323945000, 36619500000, 183096375000, 915476250000, 4577353125210, 22886625003000, 114432421904040, 572158593987000

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003948, 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 (4, 4, 4, 4, 4, 4, 4, 4, -10).

Programs

Mathematica

With[{num=Total[2t^Range[8]]+t^9+1,den=Total[-4 t^Range[8]]+10t^9+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Jan 22 2012 *)

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)/(10*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t

+ 1)