A165219 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467165, 3874204080, 34867833120, 313810465680, 2824293899520, 25418642471280, 228767758621920, 2058909615020880, 18530184622000320, 166771644379316460

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003952, 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 (8, 8, 8, 8, 8, 8, 8, 8, -36).

Formula

G.f. (t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +

1)/(36*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t

+ 1)