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A133310
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a(3n) = 2n+1, a(3n+1) = 2n+2, a(3n+2) = 2n+1.
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2
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1, 2, 1, 3, 4, 3, 5, 6, 5, 7, 8, 7, 9, 10, 9, 11, 12, 11, 13, 14, 13, 15, 16, 15, 17, 18, 17, 19, 20, 19, 21, 22, 21, 23, 24, 23, 25, 26, 25, 27, 28, 27, 29, 30, 29, 31, 32, 31, 33, 34, 33, 35, 36, 35, 37, 38, 37, 39, 40, 39, 41, 42, 41, 43, 44, 43, 45, 46, 45, 47, 48, 47, 49, 50
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OFFSET
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0,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
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FORMULA
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G.f.: ( 1+x-x^2+x^3 ) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, May 23 2014
a(n) = (2/9)*(3*n+3+3*cos[2*(n-1)*Pi/3)-2*sqrt(3)*sin(2*(n-1)*Pi/3)). - Wesley Ivan Hurt, Sep 30 2017
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MATHEMATICA
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CoefficientList[Series[(1+x-x^2+x^3)/((1+x+x^2)*(x-1)^2), {x, 0, 50}], x] (* G. C. Greubel, Feb 10 2018 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 2, 1, 3}, 74] (* Robert G. Wilson v, Feb 10 2018 *)
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PROG
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(PARI) x='x+O('x^70); Vec((1+x-x^2+x^3)/((1+x+x^2)*(x-1)^2)) \\ G. C. Greubel, Feb 10 2018
(Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 70); Coefficients(R!((1+x-x^2+x^3)/((1+x+x^2)*(x-1)^2))) // G. C. Greubel, Feb 10 2018
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CROSSREFS
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Cf. A130823(1, 1, 1, 3, 3, 3).
Sequence in context: A324749 A022466 A144254 * A077608 A002124 A097564
Adjacent sequences: A133307 A133308 A133309 * A133311 A133312 A133313
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz, Oct 18 2007
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STATUS
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approved
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