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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
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
0,2
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.
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).
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 *)
PROG
(Sage)
def A166331_list(prec):
P.<t> = 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
CROSSREFS
Sequence in context: A164706 A165185 A165757 * A166495 A166859 A167106
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved