A166367 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959552, 9663676380, 77309410752, 618475283748, 4947802251840, 39582417869568, 316659341795328, 2533274725072896, 20266197726265344, 162129581215580160

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003951, 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 (7,7,7,7,7,7,7,7,7,7,-28).

Programs

Maple

seq(coeff(series((1+t)*(1-t^11)/(1-8*t+35*t^11-28*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 13 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^11)/(1-8*t+35*t^11-28*t^12), {t,0,30}], t] (* G. C. Greubel, May 10 2016 *)
coxG[{11,28,-7}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 07 2019 *)

Sage

def A166367_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^11)/(1-8*t+35*t^11-28*t^12) ).list()
A166367_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)/(28*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).