A162744 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 7, 42, 231, 1260, 6825, 36960, 200025, 1082550, 5858475, 31704750, 171577875, 928536000, 5024998125, 27194002500, 147166963125, 796429856250, 4310074059375, 23325015131250, 126228998109375, 683118955312500

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003949, 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 (5, 5, -15).

Programs

Mathematica

coxG[{3,15,-5}] (* The coxG program is at A169452 *) (* or *) LinearRecurrence[{5,5,-15},{1,7,42,231},30] (* Harvey P. Dale, Oct 02 2021 *)

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(15*t^3 - 5*t^2 - 5*t + 1)