A164637 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861060, 81715798032, 1879463209008, 43227650455440, 994235883385008, 22867423544782608, 525950700749330736, 12096865179279290124, 278227877550453062232

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170743, 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 (22,22,22,22,22,22,-253).

Programs

Mathematica

coxG[{7,253,-22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 05 2022 *)

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(253*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).