A166430 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992187500, 99307704726561870, 3475769665429643400, 121651938290036747880, 4257817840151259186600, 149023624405293126909000

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170755, 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 (34,34,34,34,34,34,34,34,34,34,-595).

Crossrefs

Cf. A154638, A169452, A170755.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-35*x+629*x^11-595*x^12) )); // G. C. Greubel, Jul 25 2024

Mathematica

With[{p=595, q=34}, 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 *)
coxG[{11, 595, -34, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jul 25 2024 *)

SageMath

def A166430_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-35*x+629*x^11-595*x^12) ).list()
A166430_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)/(595*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

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

a(n) = 34*Sum_{j=1..10} a(n-j) - 595*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 35*x + 629*x^11 - 595*x^12). (End)