A168940 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

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

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.

First disagreement at index 22: a(22) = 356947326335320446369221574403, A170742(22) = 356947326335320446369221574656. - Klaus Brockhaus, Apr 09 2011

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, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).

Crossrefs

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

Programs

Mathematica

coxG[{22,231,-21}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 04 2018 *)

Formula

G.f.: (t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*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^22 - 21*t^21 - 21*t^20 - 21*t^19 - 21*t^18 - 21*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).