A168700 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192009216, 610878224202752, 13439320932460544, 295665060514131968, 6504631331310903296, 143101889288839872512

Offset

0,2

Comments

The initial terms coincide with those of A170742, although the two sequences are eventually different.

First disagreement at index 17: a(17) = 69261314415798498295555, A170742(17) = 69261314415798498295808. - Klaus Brockhaus, Mar 30 2011

Computed with MAGMA using commands similar to those used to compute A154638.

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

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

Formula

G.f.: (t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/ (231*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 -21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 -21*t^5 -21*t^4 -21*t^3 -21*t^2 -21*t +1).

Mathematica

CoefficientList[Series[(t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(231*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 04 2016 *)
coxG[{17, 231, -21}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 18 2024 *)

Crossrefs

Cf. A170742 (G.f.: (1+x)/(1-22*x)).

Sequence in context: A167174 A167694 A167937 * A168748 A168796 A168844

Adjacent sequences: A168697 A168698 A168699 * A168701 A168702 A168703

Keyword

nonn

Author

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

Status

approved