A164742 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959531, 11757060, 70541625, 423245340, 2539445580, 15236514720, 91418135760, 548503099200, 3290984303460, 19745700072525, 118472965958550, 710830388968875, 4264937893581750

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, -15).

Programs

Mathematica

coxG[{8,15,-5}] (* The coxG program is at A169452 *)  (* Harvey P. Dale, Dec 19 2024 *)

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)/(15*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).