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A011658 Period 5: repeat [0, 0, 0, 1, 1]; also expansion of 1/(x^4 + x^3 + x^2 + x + 1) (mod 2). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

LINKS

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).

FORMULA

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

MATHEMATICA

PadRight[{}, 120, {0, 0, 0, 1, 1}] (* Harvey P. Dale, Dec 16 2015 *)

PROG

(PARI) a(n)=(n%5)\3 \\ Charles R Greathouse IV, Jan 16 2017

CROSSREFS

Cf. A198517. Parity of A010891(n+2).

Sequence in context: A288710 A179827 A285133 * A135461 A327219 A274950

Adjacent sequences:  A011655 A011656 A011657 * A011659 A011660 A011661

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 15 12:09 EDT 2022. Contains 356145 sequences. (Running on oeis4.)