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A166367
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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.
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1
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1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959552, 9663676380, 77309410752, 618475283748, 4947802251840, 39582417869568, 316659341795328, 2533274725072896, 20266197726265344, 162129581215580160
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (7,7,7,7,7,7,7,7,7,7,-28).
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FORMULA
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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).
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^11)/(1-8*t+35*t^11-28*t^12) ).list()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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