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A152822 Periodic sequence [1,1,0,1] of length 4. 6
1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for characteristic functions

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

FORMULA

a(n) = 3/4 - (1/4)*(-1)^n + (1/2)*cos(n*Pi/2);

a(n+4) = a(n) with a(0) = a(1) = a(3) = 1 and a(2) = 0;

O.g.f.: (1+z+z^3)/(1-z^4);

From Paolo P. Lava, Dec 15 2008: (Start)

a(n) = (1/8)*((n mod 4) - ((n+1) mod 4) + 3*((n+2) mod 4)((n+3) mod 4)), with n >= 0.

a(n) = (1/4)*(3 + i^n + (-i)^n - (-1)^n), with n >= 0 and i = sqrt(-1). (End)

a(n) = ceiling(cos(Pi*n/4)^2). - Wesley Ivan Hurt, Jun 12 2013

From Antti Karttunen, May 03 2022: (Start)

Multiplicative with a(p^e) = 1 for odd primes, and a(2^e) = [e > 1]. (Here [ ] is the Iverson bracket, i.e., a(2^e) = 0 if e=1, and 1 if e>1).

a(n) = A166486(2+n).

(End)

MAPLE

a:= n-> [1, 1, 0, 1][1+irem(n, 4)]:

seq(a(n), n=0..104);  # Alois P. Heinz, Sep 01 2021

PROG

(PARI) a(n)=n%4!=2 \\ Jaume Oliver Lafont, Mar 24 2009

(PARI) A152822(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], f[k, 2]>1, 1)); }; \\ (After multiplicative formula) - Antti Karttunen, May 03 2022

CROSSREFS

Characteristic function of A042965.

Cf. A026052, A026064, A320111 (inverse Möbius transform).

Sequence A166486 shifted by two terms.

Sequence in context: A085369 A188082 A046980 * A118831 A118828 A105234

Adjacent sequences:  A152819 A152820 A152821 * A152823 A152824 A152825

KEYWORD

easy,nonn,mult

AUTHOR

Richard Choulet, Dec 13 2008

EXTENSIONS

More terms from Philippe Deléham, Dec 21 2008

Keyword:mult added by Andrew Howroyd, Jul 27 2018

STATUS

approved

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Last modified July 2 13:59 EDT 2022. Contains 355007 sequences. (Running on oeis4.)