A166331 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242870, 20971440, 83885610, 335541840, 1342164960, 5368650240, 21474562560, 85898096640, 343591772160, 1374364631040, 5497448693760, 21989755453530, 87958864528380

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003947, 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..1000
• Index entries for linear recurrences with constant coefficients, signature (3,3,3,3,3,3,3,3,3,3,-6).

Programs

Maple

seq(coeff(series((1+t)*(1-t^11)/(1-4*t+9*t^11-6*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 13 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^11)/(1-4*t+9*t^11-6*t^12), {t,0,30}], t] (* G. C. Greubel, May 09 2016 *)
coxG[{11, 6, -3}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 13 2020 *)

Sage

def A166331_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^11)/(1-4*t+9*t^11-6*t^12) ).list()
A166331_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)/(6*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).