A165692 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717440000000, 268697599999180, 10747903999934400, 429916159996064820, 17196646399790145600, 687865855989507936000, 27514634239496401920000

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170760, 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 (39, 39, 39, 39, 39, 39, 39, 39, -780).

Programs

Mathematica

With[{num=Total[2t^Range[8]]+t^9+1,den=Total[-39 t^Range[8]]+ 780t^9+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Jul 20 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)/(780*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 -

39*t^2 - 39*t + 1)