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A163503
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Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
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1
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1, 21, 420, 8400, 168000, 3359790, 67191600, 1343748210, 26873288400, 537432252000, 10747974763890, 214946090593500, 4298653734898110, 85967713492846500, 1719247052441058000, 34382796834223386990
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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 A170740, 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)/(190*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).
a(n) = 19*a(n-1)+19*a(n-2)+19*a(n-3)+19*a(n-4)-190*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)/(1-20*x+209*x^5-190*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 26 2017 *)
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PROG
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(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6)) \\ G. C. Greubel, Jul 26 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6) )); // G. C. Greubel, May 16 2019
(Sage) ((1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 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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