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A163223
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Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
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1
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1, 40, 1560, 60840, 2371980, 92476800, 3605409600, 140564736000, 5480222014020, 213658376756760, 8329936604744040, 324760699264187160, 12661502336823753660, 493636212105145265520, 19245481572342746507280
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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 A170759, 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)/(741*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).
a(n) = 38*a(n-1)+38*a(n-2)+38*a(n-3)-741*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)/(741*t^4-38*t^3-38*t^2 - 38*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[{38, 38, 38, -741}, {40, 1560, 60840, 2371980}, 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)/(741*t^4- 38*t^3 -38*t^2-38*t+1)) \\ G. C. Greubel, Dec 11 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-39*x+779*x^4-741*x^5) )); // G. C. Greubel, Apr 30 2019
(Sage) ((1+x)*(1-x^4)/(1-39*x+779*x^4-741*x^5)).series(x, 20).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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