A166434 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749750440, 5489240267160, 214080370419240, 8349134446350360, 325616243407663260, 12699033492898836720, 495262306223053446480, 19315229942699038174320

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..500
• Index entries for linear recurrences with constant coefficients, signature (38,38,38,38,38,38,38,38,38,38,-741).

Crossrefs

Cf. A154638, A169452, A170759.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-39*x+779*x^11-741*x^12) )); // G. C. Greubel, Jul 25 2024

Mathematica

coxG[{11,741,-38}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 10 2015 *)
With[{p=741, q=38}, 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 14 2016; Jul 25 2024 *)

SageMath

def A166434_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-39*x+779*x^11-741*x^12) ).list()
A166434_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)/(741*t^11 - 38*t^10 - 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).

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

a(n) = 38*Sum_{j=1..10} a(n-j) - 741*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 39*x + 779*x^11 - 741*x^12). (End)