A166439 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501434880, 632170063134720, 27815482777927680, 1223881242228816930, 53850774658067901360, 2369434084954985744190, 104255099738019288455760

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170764, 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 (43,43,43,43,43,43,43,43,43,43,-946).

Crossrefs

Cf. A154638, A169452, A170764.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
f:= func< p,q,x | (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12) >;
Coefficients(R!( f(946,43,x) )); // G. C. Greubel, Jul 26 2024

Mathematica

coxG[{11,946,-43}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 08 2015 *)
With[{p=946, q=43}, 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 26 2024 *)

SageMath

def f(p,q,x): return (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12)
def A166439_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( f(946,43,x) ).list()
A166439_list(30) # G. C. Greubel, Jul 26 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)/(946*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).

From G. C. Greubel, Jul 26 2024: (Start)

a(n) = 43*Sum_{j=1..10} a(n-j) - 946*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 44*x + 989*x^11 - 946*x^12). (End)