A165308 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006249880, 615093746400, 9226406169120, 138396092133600, 2075941375956000, 31139120548620000, 467086806868500000, 7006302082615500000

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170735, 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 (14, 14, 14, 14, 14, 14, 14, 14, -105).

Programs

Mathematica

coxG[{9,105,-14}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 14 2021 *)

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)/(105*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 -

14*t^2 - 14*t + 1)