A162882 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 44, 1892, 80410, 3416952, 145180728, 6168492330, 262088760780, 11135706433236, 473137249574682, 20102798001348216, 854133737629549608, 36290691560131770762, 1541929835910758016492, 65513979388697887768644

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

The initial terms coincide with those of A170763, 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..612
• Index entries for linear recurrences with constant coefficients, signature (42, 42, -903).

Programs

GAP

a:=[44,1892,80410];; for n in [4..20] do a[n]:=42*a[n-1]+42*a[n-2] -903*a[n-3]; od; Concatenation([1],a); # Muniru A Asiru, Oct 24 2018

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(903*t^3-42*t^2-42*t+1))); // G. C. Greubel, Oct 24 2018

Maple

seq(coeff(series((x^3+2*x^2+2*x+1)/(903*x^3-42*x^2-42*x+1),x,n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 24 2018

Mathematica

CoefficientList[Series[(t^3+2*t^2+2*t+1)/(903*t^3-42*t^2-42*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *)
coxG[{3, 903, -42}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 27 2019 *)

PARI

my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(903*t^3-42*t^2-42*t+1)) \\ G. C. Greubel, Oct 24 2018

Sage

((1+x)*(1-x^3)/(1 -43*x +945*x^3 -903*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 27 2019

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(903*t^3 - 42*t^2 - 42*t + 1).

a(n) = 42*a(n-1) + 42*a(n-2) - 903*a(n-3), n > 0. - Muniru A Asiru, Oct 24 2018

G.f.: (1+x)*(1-x^3)/(1 - 43*x + 945*x^3 - 903*x^4). - G. C. Greubel, Apr 27 2019