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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
1, 6, 30, 150, 750, 3750, 18750, 93750, 468750, 2343750, 11718750, 58593735, 292968600, 1464842640, 7324211400, 36621048000, 183105195000, 915525750000, 4577627625000, 22888132500000, 114440634375000, 572203031250000
OFFSET
0,2
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.
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).
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 *)
PROG
(Sage)
def A166364_list(prec):
P.<t> = 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
CROSSREFS
Sequence in context: A164741 A165213 A165777 * A166500 A166877 A167107
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved