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

0,2

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

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (21,21,21,21,21,21,-231).

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).

Mathematica

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

Crossrefs

Sequence in context: A163171 A163518 A163991 * A164957 A165365 A165939

Adjacent sequences: A164633 A164634 A164635 * A164637 A164638 A164639

Keyword

nonn

Author

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

Status

approved