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A163441
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Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
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1
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1, 16, 240, 3600, 54000, 809880, 12146400, 182169120, 2732133600, 40975956000, 614548634280, 9216869130000, 138232634196720, 2073183516810000, 31093163487414000, 466328623499110680, 6993897072666789600
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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 A170735, 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)/(105*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).
a(n) = 14*a(n-1)+14*a(n-2)+14*a(n-3)+14*a(n-4)-105*a(n-5). - Wesley Ivan Hurt, May 10 2021
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1-x^5)/(1-15*x+119*x^5-105*x^6), {x, 0, 20}], x] (* or *) LinearRecurrence[{14, 14, 14, 14, -105}, {1, 16, 240, 3600, 54000, 809880}, 20] (* G. C. Greubel, Dec 23 2016 *)
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PROG
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(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-15*x+119*x^5-105*x^6)) \\ G. C. Greubel, Dec 23 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-15*x+119*x^5-105*x^6) )); // G. C. Greubel, May 13 2019
(Sage) ((1+x)*(1-x^5)/(1-15*x+119*x^5-105*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 13 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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