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A163677
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Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
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1
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1, 41, 1640, 65600, 2624000, 104959180, 4198334400, 167932064820, 6717230145600, 268687107936000, 10747400402591580, 429892659535950000, 17195572119777744420, 687817514366631090000, 27512485759363357584000
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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 A170760, 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^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).
a(n) = 39*a(n-1)+39*a(n-2)+39*a(n-3)+39*a(n-4)-780*a(n-5). - Wesley Ivan Hurt, May 11 2021
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1-x^5)/(1-40*x+819*x^5-780*x^6), {x, 0, 20}], x] (* G. C. Greubel, Aug 02 2017 *)
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PROG
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(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-40*x+819*x^5-780*x^6)) \\ G. C. Greubel, Aug 02 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-40*x+819*x^5-780*x^6) )); // G. C. Greubel, May 24 2019
(Sage) ((1+x)*(1-x^5)/(1-40*x+819*x^5-780*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 24 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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