A164671 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068153965, 1838317214580, 62502784608495, 2125094653323180, 72253217418556020, 2456609365220213280, 83524717499123743920, 2839840363745848388310, 96554571305730654116385

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,-561).

Programs

Mathematica

coxG[{7,561,-33}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 11 2025 *)

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).