A164665 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 29, 812, 22736, 636608, 17825024, 499100672, 13974818410, 391294904112, 10956256997238, 306775187021520, 8589704987370528, 240511732667877888, 6734328319302667776, 188561187469333295694, 5279713095949377473052

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170748, 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 (27,27,27,27,27,27,-378).

Programs

Mathematica

coxG[{7,378,-27}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 19 2019 *)

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(378*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).