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A100286
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Expansion of (1+2*x^2-2*x^3+2*x^4)/(1-x+x^2-x^3+x^4-x^5).
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2
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1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5).
a(n) = (1/6)*(6 + 3*cos(Pi*n/3) - 3*cos(2*Pi*n/3) + sqrt(3)*sin(Pi*n/3) - 3*sqrt(3)*sin(2*Pi*n/3)).
a(n) = a(n-6).
a(n) = 2 + (n mod 2)*(1 - (n-1 mod 3)) - (n+1 mod 3). (End)
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MATHEMATICA
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CoefficientList[Series[(1+2x^2-2x^3+2x^4)/(1-x+x^2-x^3+x^4-x^5), {x, 0, 100}], x] (* Harvey P. Dale, Mar 03 2019 *)
PadRight[{}, 120, {1, 1, 2, 0, 0, 2}] (* G. C. Greubel, Feb 06 2023 *)
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PROG
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(Magma) [2 +(n mod 2)*(1-((n+2) mod 3)) -((n+1) mod 3): n in [0..100]]; // G. C. Greubel, Feb 06 2023
(SageMath)
def A100286(n): return 2 +(n%2)*(1-((n-1)%3)) -((n+1)%3)
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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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STATUS
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approved
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