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A163231
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Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
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1
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1, 45, 1980, 87120, 3832290, 168577200, 7415481150, 326196882000, 14348955088710, 631190926398780, 27765226324720170, 1221354364616557380, 53725709508796162530, 2363320544672336677560, 103959241263364038810390
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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 A170764, 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^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
a(n) = 43*a(n-1)+43*a(n-2)+43*a(n-3)-946*a(n-4). - Wesley Ivan Hurt, May 06 2021
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MATHEMATICA
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CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(946*t^4-43*t^3-43*t^2 - 43*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[ {43, 43, 43, -946}, {45, 1980, 87120, 3832290}, 20]] (* G. C. Greubel, Dec 11 2016 *)
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PROG
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(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(946*t^4-43*t^3 - 43*t^2-43*t+1)) \\ G. C. Greubel, Dec 11 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^4)/(1-44*x+989*x^4-946*x^5) )); // G. C. Greubel, Apr 30 2019
(Sage) ((1+x)*(1-x^4)/(1-44*x+989*x^4-946*x^5)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 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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