A169180 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = 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 27: a(27) = 1839575163316150182662704122237550339, A170742(27) = 1839575163316150182662704122237550592. - Klaus Brockhaus, May 07 2011

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

Formula

G.f.: (t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*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^27 - 21*t^26 - 21*t^25 - 21*t^24 - 21*t^23 - 21*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).

Mathematica

coxG[{27, 231, -21}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 23 2016 *)

Crossrefs

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

Sequence in context: A169036 A169084 A169132 * A169228 A169276 A169324

Adjacent sequences: A169177 A169178 A169179 * A169181 A169182 A169183

Keyword

nonn

Author

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

Status

approved