A166610 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192009216, 610878224202752, 13439320932460291, 295665060514120836, 6504631331310536193, 143101889288829107868

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

• 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, -231).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13) )); // G. C. Greubel, Apr 25 2019

Mathematica

coxG[{12,231,-21}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 03 2015 *)
CoefficientList[Series[(1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13), {x, 0, 20}], x] (* G. C. Greubel, May 18 2016, modified Apr 25 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13)) \\ G. C. Greubel, Apr 25 2019

Sage

((1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

Formula

G.f.: (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^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).

G.f.: (1+x)*(1-x^12)/(1 -22*x + 252*x^12 - 231*x^13). - G. C. Greubel, Apr 25 2019