A162754 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 8, 56, 364, 2352, 15120, 97188, 624456, 4012344, 25779852, 165639600, 1064257488, 6838005636, 43935147144, 282289509432, 1813749821100, 11653597893168, 74876006587536, 481088880641124, 3091063767615432

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003950, 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 (6, 6, -21).

Programs

Mathematica

coxG[{3,21,-6}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 23 2025 *)

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(21*t^3 - 6*t^2 - 6*t + 1)