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

0,2

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

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (14, 14, 14, 14, 14, 14, 14, -105).

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)

Mathematica

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

Crossrefs

Sequence in context: A163441 A163964 A164627 * A063814 A165308 A165876

Adjacent sequences: A164864 A164865 A164866 * A164868 A164869 A164870

Keyword

nonn

Author

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

Status

approved