A166075 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610172999999535, 18305189999972100, 549155699998744965, 16474670999949807900, 494240129998118005500, 14827203899932253220000

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170750, 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..500
• Index entries for linear recurrences with constant coefficients, signature (29,29,29,29,29,29,29,29,29,-435).

Programs

GAP

a:=[31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610172999999535];; for n in [11..30] do a[n]:=29*Sum([1..9], j-> a[n-j]) - 435*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Dec 05 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11) )); // G. C. Greubel, Dec 05 2019

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Dec 05 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11), {t,0,30}], t] (* G. C. Greubel, Apr 24 2016 *)

PARI

my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11)) \\ G. C. Greubel, Dec 05 2019

Sage

def A166075_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-30*t+464*t^10-435*t^11)).list()
A166075_list(30) # G. C. Greubel, Dec 05 2019

Formula

G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).