A165650 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786670765, 2125094746785780, 72253221390029295, 2456609527237630380, 83524723925285000820, 2839840613432679336480, 96554580855792733932720

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170754, 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 (33, 33, 33, 33, 33, 33, 33, 33, -561).

Programs

Mathematica

coxG[{9,561,-33}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 14 2022 *)

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)/(561*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 -

33*t^2 - 33*t + 1)