A163230 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 44, 1892, 81356, 3497362, 150345888, 6463124976, 277839201024, 11943854101410, 513446807614356, 22072240836651852, 948849634132915284, 40789498214388049434, 1753474001285744132472, 75378987430163637459624

Offset: 0

Author

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

Keywords

• nonn

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..600
• Index entries for linear recurrences with constant coefficients, signature (42, 42, 42, -903).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-43*x+945*x^4-903*x^5) )); // G. C. Greubel, Apr 30 2019

Mathematica

coxG[{4,903,-42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 18 2015 *)
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(903*t^4-42*t^3-42*t^2 - 42*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {42, 42, 42, -903}, {44,1892,81356,3497362}, 50]] (* G. C. Greubel, Dec 11 2016 *)

PARI

my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(903*t^4-42*t^3 - 42*t^2-42*t+1)) \\ G. C. Greubel, Dec 11 2016

Sage

((1+x)*(1-x^4)/(1-43*x+945*x^4-903*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(903*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).

a(n) = 42*a(n-1)+42*a(n-2)+42*a(n-3)-903*a(n-4). - Wesley Ivan Hurt, May 06 2021