A165687 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 38, 1406, 52022, 1924814, 71218118, 2635070366, 97497603542, 3607411331054, 133474219248295, 4938546112160904, 182726206148991744, 6760869627477111480, 250152176215336551984, 9255630519918739230696

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170757, 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 (36, 36, 36, 36, 36, 36, 36, 36, -666).

Programs

Mathematica

coxG[{9,666,-36}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 09 2018 *)

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)/(666*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 -

36*t^2 - 36*t + 1)