A164630 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476089, 7386090912, 125563501440, 2134578775392, 36287826447168, 616892833115424, 10487174482692864, 178281903641223096, 3030791298303722112, 51523433990019421056

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170737, 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 (16,16,16,16,16,16,-136).

Programs

Mathematica

coxG[{7,136,-16}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 17 2023 *)

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(136*t^7 - 16*t^6 -16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).