A165177 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501433890, 632170063047600, 27815482772178750, 1223881241891576400, 53850774639520663200, 2369434083975726451200, 104255099687751923750400

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170764, 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 (43, 43, 43, 43, 43, 43, 43, -946).

Programs

Mathematica

coxG[{8,946,-43}] (* The coxG program is at A169452 *)  (* Harvey P. Dale, May 18 2023 *)

Formula

G.f. (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^8 -

43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1)