A166429 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392091565, 2456609527331092980, 83524723929256474095, 2839840613594696753580, 96554580862218895189620

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170754, 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 (33,33,33,33,33,33,33,33,33,33,-561).

Crossrefs

Cf. A154638, A169452, A170754.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-34*x+594*x^11-561*x^12) )); // G. C. Greubel, Jul 25 2024

Mathematica

With[{p=561, q=33}, 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, 561, -33, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jul 25 2024 *)

SageMath

def A166429_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-34*x+594*x^11-561*x^12) ).list()
A166429_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)/(561*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

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

a(n) = 33*Sum_{j=1..10} a(n-j) - 561*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 34*x + 594*x^11 - 561*x^12). (End)