A166365 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543872, 423263211, 2539579140, 15237474105, 91424840220, 548549014860, 3291293930400, 19747762629840, 118486570063680, 710919386089920, 4265516110786560

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003949, 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 (5,5,5,5,5,5,5,5,5,5,-15).

Programs

Maple

seq(coeff(series((1+t)*(1-t^11)/(1-6*t+20*t^11-15*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 13 2020

Mathematica

CoefficientList[Series[(1+t)*(1-t^11)/(1-6*t+20*t^11-15*t^12), {t,0,30}], t] (* G. C. Greubel, May 10 2016 *)
coxG[{11, 15, -5}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 13 2020 *)

Sage

def A166365_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^11)/(1-6*t+20*t^11-15*t^12) ).list()
A166365_list(30) # G. C. Greubel, Aug 10 2019

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)/(15*t^11 - 5*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).