A164867 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733749880, 41006246400, 615093669120, 9226404633600, 138396063456000, 2075940861120000, 31139111556000000, 467086652928000000, 7006299487740014280

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170735, 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 (14, 14, 14, 14, 14, 14, 14, -105).

Programs

Mathematica

coxG[{8,105,-14}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 16 2015 *)

Formula

G.f. (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^8 -

14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1)