A165172 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749750440, 5489240266380, 214080370358400, 8349134442792000, 325616243222649600, 12699033483880036800, 495262305800992828800, 19315229923495904673600

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, 38, -741).

Formula

G.f.: (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(741*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).

a(n) = -741*a(n-8) + 38*Sum_{k=1..7} a(n-k). - Wesley Ivan Hurt, Apr 25 2023