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A164369
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Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
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2
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1, 7, 42, 252, 1512, 9072, 54432, 326571, 1959300, 11755065, 70525980, 423129420, 2538617760, 15230754000, 91378809060, 548238566925, 3289225689750, 19734119944875, 118397314970550, 710339464409400, 4261770250642800
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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 A003949, 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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FORMULA
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G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
G.f.: (1+x)*(1-x^7)/(1 -6*x +20*x^7 -15*x^8). - G. C. Greubel, Apr 25 2019
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8), {x, 0, 30}], x] (* G. C. Greubel, Sep 17 2017, modified Apr 25 2019 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8)) \\ G. C. Greubel, Sep 17 2017, modified Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
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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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