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

0,2

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).

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

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 *)

Prog

(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<x>:=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
(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

Crossrefs

Sequence in context: A132123 A190944 A115822 * A190871 A097784 A352574

Adjacent sequences: A162757 A162758 A162759 * A162761 A162762 A162763

Keyword

nonn

Author

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

Status

approved