A163991 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 23, 506, 11132, 244904, 5387888, 118533283, 2607726660, 57369864321, 1262134326684, 27766896042732, 610870411765152, 13439120433048156, 295660019761129485, 6504506579923898238, 143098839952914095019, 3148167773259336785958, 69259543486514630343864

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..740
• Index entries for linear recurrences with constant coefficients, signature (21,21,21,21,21,-231).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7) )); // G. C. Greubel, Apr 25 2019

Mathematica

CoefficientList[Series[(1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7), {x,0,20}], x] (* G. C. Greubel, Aug 24 2017, modified Apr 25 2019 *)
coxG[{6, 231, -21}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 25 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7)) \\ G. C. Greubel, Aug 24 2017, modified Apr 25 2019

Sage

((1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

Formula

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(231*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).

G.f.: (1+x)*(1-x^6)/(1 -22*x +252*x^6 -231*x^7). - G. C. Greubel, Apr 25 2019