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A095130
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Expansion of (x+x^2)/(1-x^6); period 6: repeat [0, 1, 1, 0, 0, 0].
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3
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0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1
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OFFSET
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0,1
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COMMENTS
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Sequences of period k composed of (k-p) zeros followed by p ones have a closed formula of floor((n mod k)/(k-p)), for p>=floor(n/2). [Gary Detlefs, May 18 2011]
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LINKS
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FORMULA
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G.f.: x/(1-x+x^2-x^3+x^4-x^5);
a(n) = 1/3-cos(2*Pi*n/3)/3+sin(Pi*n/3)/sqrt(3).
a(0)=0, a(1)=1, a(2)=1, a(3)=0, a(4)=0, a(n) = a(n-1)-a(n-2)+a(n-3)-a(n-4)+ a(n-5). - Harvey P. Dale, Nov 18 2013
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MAPLE
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MATHEMATICA
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PadRight[{}, 120, {0, 1, 1, 0, 0, 0}] (* or *) LinearRecurrence[{1, -1, 1, -1, 1}, {0, 1, 1, 0, 0}, 120] (* Harvey P. Dale, Nov 18 2013 *)
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PROG
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(Magma) [Floor(((n+3) mod 6)/4) : n in [0..100]]; // Wesley Ivan Hurt, Sep 08 2015
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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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