A166425 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610173000000000, 18305189999999535, 549155699999972100, 16474670999998744965, 494240129999949807900, 14827203899998118005500

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 (29,29,29,29,29,29,29,29,29,29,-435).

Crossrefs

Cf. A154638, A169452, A170750.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-30*x+464*x^11-435*x^12) )); // G. C. Greubel, Jul 25 2024

Mathematica

With[{p=435, q=29}, CoefficientList[Series[(1+t)*(1-t^11)/(1-(q+1)*t + (p+q)*t^11-p*t^12), {t,0,40}], t]] (* G. C. Greubel, May 13 2016; Jul 25 2024 *)
coxG[{11,435,-29}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 26 2021 *)

SageMath

def A166425_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-30*x+464*x^11-435*x^12) ).list()
A166425_list(30) # G. C. Greubel, Jul 25 2024

Formula

G.f.: (t^11 + 2*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^11 - 29*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).

From G. C. Greubel, Jul 25 2024: (Start)

a(n) = 29*Sum_{j=1..10} a(n-j) - 435*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 30*x + 464*x^11 - 435*x^12). (End)