A162807 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 21, 420, 8190, 159600, 3108210, 60532290, 1178845500, 22957618110, 447091673490, 8706955895400, 169564956368010, 3302218915041690, 64309571936658300, 1252406684472377910, 24390187277913766890

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170740, 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 (19, 19, -190).

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(190*t^3 - 19*t^2 - 19*t + 1).

a(n) = 19*a(n-1)+19*a(n-2)-190*a(n-3). - Wesley Ivan Hurt, May 02 2021