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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
1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959552, 9663676380, 77309410752, 618475283748, 4947802251840, 39582417869568, 316659341795328, 2533274725072896, 20266197726265344, 162129581215580160
OFFSET
0,2
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.
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).
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 *)
PROG
(Sage)
def A166367_list(prec):
P.<t> = 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
CROSSREFS
Sequence in context: A164777 A165216 A165787 * A166541 A166924 A167110
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved