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A132951
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Period 6: repeat [1, 3, 1, -1, -3, -1].
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1
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1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 3*a(n-1)-a(n-3)+3*a(n-4).
O.g.f.: (1+3*x+x^2)/((x+1)*(x^2-x+1)) = -(1/3)/(x+1)+(1/3)*(4*x+4)/(x^2-x+1). - R. J. Mathar, Nov 28 2007
a(n) = -(1/3)*(-1)^n+(4/3)*cos(Pi*n/3)+(4*3^0.5/3)*sin(Pi*n/3). - Richard Choulet, Jan 02 2008
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MATHEMATICA
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PadRight[{}, 120, {1, 3, 1, -1, -3, -1}] (* Harvey P. Dale, Feb 26 2024 *)
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PROG
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(Magma) &cat [[1, 3, 1, -1, -3, -1]: n in [0..20]]; // Wesley Ivan Hurt, Nov 18 2022
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CROSSREFS
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KEYWORD
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sign,easy,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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