OFFSET
0,1
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..65537
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);
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)
Dirichlet g.f.: zeta(s)*(1 - 1/2^s + 1/4^s). - Amiram Eldar, Dec 27 2022
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
(Python)
def A152822(n): return (1, 1, 0, 1)[n&3] # Chai Wah Wu, Jan 10 2023
CROSSREFS
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