A164636 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737539, 57370220292, 1262144724225, 27767181244572, 610877928236268, 13439313120022944, 295664860014655824, 6504626290553815116, 143101764537275790477

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170742, 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 (21,21,21,21,21,21,-231).

Programs

Mathematica

coxG[{7,231,-21}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 26 2020 *)

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(231*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).