A166411 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 17, 272, 4352, 69632, 1114112, 17825792, 285212672, 4563402752, 73014444032, 1168231104512, 18691697672056, 299067162750720, 4785074603976840, 76561193663074560, 1224979098600314880, 19599665577462988800

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170736, 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 (15,15,15,15,15,15,15,15,15,15,-120).

Crossrefs

Cf. A154638, A169452, A170736.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-16*x+135*x^11-120*x^12) )); // G. C. Greubel, Jul 23 2024

Mathematica

With[{p=120, q=15}, 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 12 2016; Jul 23 2024 *)
coxG[{11,120,-15}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 29 2016 *)

SageMath

def A166411_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-16*x+135*x^11-120*x^12) ).list()
A166411_list(30) # G. C. Greubel, Jul 23 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)/(120*t^11 - 15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).

From G. C. Greubel, Jul 23 2024: (Start)

a(n) = 15*Sum_{j=1..10} a(n-j) - 120*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 16*x + 135*x^11 - 120*x^12). (End)