A162877 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 40, 1560, 60060, 2311920, 88979280, 3424561140, 131801403240, 5072652999960, 195231667516860, 7513899339838320, 289188142406526480, 11130010920731869140, 428361764988438838440, 16486399071025250766360

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170759, 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..615
• Index entries for linear recurrences with constant coefficients, signature (38, 38, -741).

Programs

GAP

a:=[40,1560,60060];; for n in [4..20] do a[n]:=38*a[n-1]+38*a[n-2] -741*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)/(741*t^3-38*t^2-38*t+1))); // G. C. Greubel, Oct 24 2018

Maple

seq(coeff(series((x^3+2*x^2+2*x+1)/(741*x^3-38*x^2-38*x+1),x,n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 24 2018

Mathematica

coxG[{3,741,-38}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 29 2017 *)
CoefficientList[Series[(t^3+2*t^2+2*t+1)/(741*t^3-38*t^2-38*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *)

PARI

my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(741*t^3-38*t^2-38*t+1)) \\ G. C. Greubel, Oct 24 2018

Sage

((1+x)*(1-x^3)/(1 -39*x +779*x^3 -741*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)/(741*t^3 - 38*t^2 - 38*t + 1).

a(n) = 38*a(n-1) + 38*a(n-2) - 741*a(n-3), n > 0. - Muniru A Asiru, Oct 24 2018

G.f.: (1+x)*(1-x^3)/(1 - 39*x + 779*x^3 - 741*x^4). - G. C. Greubel, Apr 27 2019