A165214 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757291, 70543620, 423260985, 2539561500, 15237342540, 91423896480, 548542426320, 3291248842560, 19747458763200, 118484546826660, 710906046446925, 4265428871616150

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003949, 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 (5, 5, 5, 5, 5, 5, 5, 5, -15).

Programs

Mathematica

coxG[{9,15,-5}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 02 2015 *)

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)/(15*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t

+ 1)