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

0,2

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).

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

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 *)

Prog

(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
(Magma) R<x>:=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
(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

Crossrefs

Sequence in context: A278793 A004295 A162882 * A163748 A164277 A164688

Adjacent sequences: A163227 A163228 A163229 * A163231 A163232 A163233

Keyword

nonn

Author

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

Status

approved