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A164332
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Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
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2
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1, 47, 2162, 99452, 4574792, 210440432, 9680258791, 445291854660, 20483423028045, 942237354119580, 43342913451658140, 1993773796235517600, 91713584389960162440, 4218824411042032288125, 194065901246713684538250
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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 A170766, 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^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
G.f.: (1+x)*(1-x^6)/(1 -46*x +1080*x^6 -1035*x^7). - G. C. Greubel, Apr 25 2019
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7), {x, 0, 20}], x] (* G. C. Greubel, Sep 14 2017, modified Apr 25 2019 *)
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PROG
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(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7)) \\ G. C. Greubel, Sep 14 2017, modified Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7)).series(x, 20).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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