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A011658
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Period 5: repeat [0, 0, 0, 1, 1]; also expansion of 1/(x^4 + x^3 + x^2 + x + 1) (mod 2).
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4
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0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0
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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(k/2). - Gary Detlefs, May 18 2011
a(n+3) is the determinant of an n X n pentadiagonal symmetric Toeplitz matrix with a=b=c=1. - R. J. Mathar, Jan 31 2023
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LINKS
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FORMULA
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a(n+4) = abs(a(n) - a(n+1) + a(n+2) - a(n+3)). - Benjamin Knight, May 06 2018
a(n) = (2/5) * (1 + cos(4*(n-4)*Pi/5) + cos(2*(n-3)*Pi/5) + cos(4*(n-3)*Pi/5) + cos(2*(n+1)*Pi/5)). - Wesley Ivan Hurt, Sep 26 2018
G.f.: -x^3*(1+x) / ( (x-1)*(1+x+x^2+x^3+x^4) ). - R. J. Mathar, Aug 11 2021
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MAPLE
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seq(floor(2*n/5) - 2*floor(n/5), n=0..100); # Ridouane Oudra, Apr 01 2023
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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