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A110568
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Period 6: repeat [1, 0, 2, 2, 0, 1].
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2
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1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 2
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OFFSET
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0,3
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COMMENTS
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Permutation of {0, 1, 2}, followed by its reversal, repeated.
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LINKS
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FORMULA
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G.f.: (1-x+3*x^2-x^3+x^4) / (1-x+x^2-x^3+x^4-x^5).
a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) for n>4.
a(n) = 1 + cos(2*Pi*n/3)/2 - sqrt(3)*sin(2*Pi*n/3)/2 - cos(Pi*n/3)/2 + sqrt(3)*sin(Pi*n/3)/6.
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MAPLE
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MATHEMATICA
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Mod[#, 3]&/@CoefficientList[Series[(1-x)/(1-x-2x^2), {x, 0, 100}], x] (* Harvey P. Dale, Mar 30 2011 *)
LinearRecurrence[{1, -1, 1, -1, 1}, {1, 0, 2, 2, 0}, 100] (* Harvey P. Dale, Apr 03 2019 *)
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PROG
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(PARI) x='x+O('x^50); Vec((1-x+3*x^2-x^3+x^4)/(1-x+x^2-x^3+x^4-x^5)) \\ G. C. Greubel, Aug 31 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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