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A166327
Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
1
1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3069, 6132, 12255, 24492, 48948, 97824, 195504, 390720, 780864, 1560576, 3118848, 6233094, 12456993, 24895608, 49754487, 99435570, 198724440, 397155696, 793725456, 1586279904, 3170219520
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003945, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1) / (t^10 - 2*t^9 + t^8 - 2*t^7 + t^6 - 2*t^5 + t^4 - 2*t^3 + t^2 - 2*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^11)/(1-2*t+2*t^11-t^12), t, n+1), t, n), n = 0..30); # G. C. Greubel, Mar 12 2020
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^11)/(1-2*t+2*t^11-t^12), {t, 0, 30}], t] (* G. C. Greubel, May 09 2016 *)
PROG
(Sage)
def A166327_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^11)/(1-2*t+2*t^11-t^12) ).list()
A166327_list(30) # G. C. Greubel, Aug 10 2019
CROSSREFS
Sequence in context: A165183 A046944 A165745 * A166467 A166857 A364496
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved