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A174443
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Generating function x/(1+4*x-8*x^2).
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2
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0, 1, -4, 24, -128, 704, -3840, 20992, -114688, 626688, -3424256, 18710528, -102236160, 558628864, -3052404736, 16678649856, -91133837312, 497964548096, -2720928890880, 14867431948288, -81237158920192, 443888091267072, -2425449636429824, 13252903275855872
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OFFSET
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0,3
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COMMENTS
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Binet form: with a = 4/(1 + sqrt(3)); b = 4/(1 - sqrt(3)); we have a(n)=(a^n - b^n)/(a - b).
Alternative expressions for the roots are -2 +- 2*sqrt(3).
Limiting ratio a(n+1)/a(n) is:-5.464101615137755== -2-2*sqrt(3).
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LINKS
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FORMULA
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a(0)=0, a(1)=1, a(n) = -4a(n-1) + 8a(n-2).
a(0)=0, a(n) = (-2)^(n-1)*A002605(n).
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MATHEMATICA
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a = 4/(1 + Sqrt[3]); b = 4/(1 - Sqrt[3]);
f[n_] = (a^n - b^n)/(a - b);
Table[FullSimplify[f[n]], {n, 0, 30}]
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CROSSREFS
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Cf. A180222 (unsigned version of this sequence).
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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Correction of the Mathematica code and better name by Joerg Arndt.
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STATUS
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approved
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