A166424 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999005595, 366015292971149640, 10614443496162974160, 307818861388715654040, 8926746980272446665760

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170749, 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 (28,28,28,28,28,28,28,28,28,28,-406).

Crossrefs

Cf. A154638, A169452, A170749.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-29*x+434*x^11-406*x^12) )); // G. C. Greubel, Jul 25 2024

Mathematica

With[{p=406, q=28}, 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[{11,406,-28}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 12 2016 *)

SageMath

def A166424_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-29*x+434*x^11-406*x^12) ).list()
A166424_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)/(406*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).

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

a(n) = 28*Sum_{j=1..10} a(n-j) - 406*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 29*x + 434*x^11 - 406*x^12). (End)