A162847 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 35, 1190, 39865, 1335180, 44708895, 1497090210, 50130334485, 1678623324840, 56209003149915, 1882168556020830, 63024751767399345, 2110395119905763460, 70666959205286686935, 2366295806989839830490, 79235839622172041773965

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, -561).

Programs

Mathematica

coxG[{3,561,-33}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 05 2016 *)

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(561*t^3 - 33*t^2 - 33*t + 1).

a(n) = 33*a(n-1) + 33*a(n-2) - 561*a(n-3). - Wesley Ivan Hurt, Apr 20 2021