A164684 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749749660, 5489240206320, 214080366860880, 8349134261335920, 325616234388803280, 12699033070834721520, 495262287019738489680, 19315229086799991370740

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170759, 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 (38,38,38,38,38,38,-741).

Programs

Mathematica

coxG[{7,741,-38}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 29 2021 *)

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(741*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).