A164969 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874401, 5638330725300, 146596598620875, 3811511557982700, 99099300347388900, 2576581804867917600, 66991126818296818800, 1741769294460722280000

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170746, 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 (25, 25, 25, 25, 25, 25, 25, -325).

Programs

Mathematica

coxG[{8,325,-25}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 23 2020 *)

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)/(325*t^8 -

25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)