A165695 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139974156, 11960018888708, 514280812213498, 22114074925139736, 950905221779260440, 40888924536433025976, 1758223755063387680376, 75603621467586675482712

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170763, 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 (42, 42, 42, 42, 42, 42, 42, 42, -903).

Programs

Mathematica

coxG[{9,903,-42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 08 2020 *)

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)/(903*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 -

42*t^2 - 42*t + 1)