A162760 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 11, 110, 1045, 9900, 93555, 884070, 8353125, 78924780, 745717995, 7045894350, 66572896005, 629011803420, 5943197049075, 56154099352230, 530570136457845, 5013074255082300, 47365865053010955, 447534797632236270

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003953, although the two sequences are eventually different.

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9, 9, -45).

Programs

Magma

I:=[1,11,110,1045]; [n le 4 select I[n] else 9*Self(n-1) +9*Self(n-2)-45*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Apr 01 2017

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^3)/(1-10*x+54*x^3-45*x^4) )); // G. C. Greubel, Apr 26 2019

Mathematica

Join[{1}, LinearRecurrence[{9, 9, -45}, {11, 110, 1045}, 19]] (* Vincenzo Librandi, Apr 01 2017 *)
CoefficientList[Series[(1+x)*(1-x^3)/(1-10*x+54*x^3-45*x^4), {x,0,20}],x] (* or *) coxG[{3, 45, -9}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)

PARI

my(x='x+O('x^20)); Vec((1+x)*(1-x^3)/(1-10*x+54*x^3-45*x^4)) \\ G. C. Greubel, Apr 26 2019

Sage

((1+x)*(1-x^3)/(1-10*x+54*x^3-45*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(45*t^3 - 9*t^2 - 9*t + 1).

G.f.: (1+x)*(1-x^3)/(1 - 10*x + 54*x^3 - 45*x^4). - G. C. Greubel, Apr 26 2019