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A107300
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a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) with a(0)=3, a(1)=2, a(3)=8.
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2
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3, 2, 8, 14, 40, 92, 236, 576, 1440, 3560, 8848, 21936, 54448, 135072, 335168, 831584, 2063360, 5119552, 12702656, 31517696, 78201600, 194033280, 481434368, 1194532096, 2963866368, 7353928192
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: (3-4*x-2*x^2)/(1-2*x-2*x^2+2*x^3). [Sep 28 2009]
a(n) = 2*(b1^n + b2^n + b3^n)/(b1 + b2 + b3), where b1, b2, and b3 and the roots of x^3 = 2*x^2 + 2*x - 2.
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MATHEMATICA
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LinearRecurrence[{2, 2, -2}, {3, 2, 8}, 46]
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PROG
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(Magma) I:=[3, 2, 8]; [n le 3 select I[n] else 2*(Self(n-1) +Self(n-2) -Self(n-3)): n in [1..46]]; // G. C. Greubel, May 02 2022
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (3-4*x-2*x^2)/(1-2*x-2*x^2+2*x^3) ).list()
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
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STATUS
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approved
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