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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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3
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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
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LINKS
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Table of n, a(n) for n=0..80.
R. Gold, Characteristic linear sequences and their coset functions, J. SIAM Applied. Math., 14 (1966), 980-985.
Index entries for characteristic functions
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).
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FORMULA
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a(n) = floor((n mod 5)/3). - Gary Detlefs, May 18 2011
a(n+2) = A198517(n+4) - A198517(n+2) + A198517(n). - Bruno Berselli, Nov 02 2011
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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MATHEMATICA
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PadRight[{}, 120, {0, 0, 0, 1, 1}] (* Harvey P. Dale, Dec 16 2015 *)
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PROG
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(PARI) a(n)=(n%5)\3 \\ Charles R Greathouse IV, Jan 16 2017
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CROSSREFS
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Cf. A198517. Parity of A010891(n+2).
Sequence in context: A288710 A179827 A285133 * A135461 A327219 A274950
Adjacent sequences: A011655 A011656 A011657 * A011659 A011660 A011661
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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