A164692 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 47, 2162, 99452, 4574792, 210440432, 9680259872, 445291953031, 20483429789700, 942237768039885, 43342937224664220, 1993775107496711580, 91713654722307975840, 4218828106989292074000, 194066092450611195098040

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170766, 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 (45, 45, 45, 45, 45, 45, -1035).

Programs

Mathematica

coxG[{7,1035,-45}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 29 2024 *)

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).