A166364 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 6, 30, 150, 750, 3750, 18750, 93750, 468750, 2343750, 11718750, 58593735, 292968600, 1464842640, 7324211400, 36621048000, 183105195000, 915525750000, 4577627625000, 22888132500000, 114440634375000, 572203031250000

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003948, 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 (4,4,4,4,4,4,4,4,4,4,-10).

Programs

Maple

seq(coeff(series((1+t)*(1-t^11)/(1-5*t+14*t^11-10*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 13 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^11)/(1-5*t+14*t^11-10*t^12), {t,0,30}], t] (* G. C. Greubel, May 10 2016 *)
coxG[{11,10,-4,30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 13 2016 *)

Sage

def A166364_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^11)/(1-5*t+14*t^11-10*t^12) ).list()
A166364_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)/(10*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).