A165693 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504378122, 8179679503002, 335366859622221, 13750041244475760, 563751691022059680, 23113819331845141200, 947666592603219256320, 38854330296632296661040

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170761, 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 (40, 40, 40, 40, 40, 40, 40, 40, -820).

Programs

Mathematica

coxG[{9,820,-40}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 05 2017 *)

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)/(820*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 -

40*t^2 - 40*t + 1)