A166366 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801964, 15818613552, 110730293520, 775112045232, 5425784250768, 37980489294384, 265863421833744, 1861043930247600, 13027307353612944

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003950, 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 (6,6,6,6,6,6,6,6,6,6,-21).

Programs

Maple

seq(coeff(series((1+t)*(1-t^11)/(1-7*t+27*t^11-21*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 13 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^11)/(1-7*t+27*t^11-21*t^12), {t,0,30}], t] (* G. C. Greubel, May 10 2016 *)
coxG[{11, 21, -6}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 13 2020 *)

Sage

def A166366_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^11)/(1-7*t+27*t^11-21*t^12) ).list()
A166366_list(30) # G. C. Greubel, Mar 13 2020

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)/(21*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).