OFFSET
0,1
COMMENTS
For periodic sequences having a period of 2*k and composed of k ones followed by k zeros we have a(n) = floor(((n+k) mod 2*k)/k). Sequences of this form are A000035(n+1) (k=1), A133872(n) (k=2), this sequence (k=3), A131078(n) (k=4), and A112713(n-1) (k=5). - Gary Detlefs, May 17 2011
LINKS
FORMULA
G.f.: (1+x+x^2)/(1-x^6) = 1/((1-x)*(1+x)*(1-x+x^2)).
a(n) = a(n-6) for n>=6, a(0)=a(1)=a(2)=1, a(3)=a(4)=a(5)=0.
a(n) = ((-1)^floor((5*n + 2)/3) + 1)/2 = ( (-1)^floor(n/3) + 1 )/2. [Simplified by Bruno Berselli, Jul 09 2013]
a(n) = Sum_{k=0..floor(n/2)} U(n-2k, 1/2). - Paul Barry, Nov 15 2003
From Paul Barry, Mar 14 2004: (Start)
Partial sums of expansion of 1/(1+x^3), see A131531.
a(n) = 2*sin(Pi*n/3 + Pi/6)/3 + cos(Pi*n)/6 + 1/2. (End)
a(n) = floor(((n+3) mod 6)/3).
a(n) = floor((5*n-1)/3) mod 2. - Gary Detlefs, May 17 2011
a(n) = 1/2 + cos(Pi*n/3)/3 + sin(Pi*n/3)/sqrt(3) + (-1)^n/6. - R. J. Mathar, Oct 08 2011
a(n) = floor(((n+2)^2)/3) mod 2. - Wesley Ivan Hurt, Jun 29 2013
a(n) = a(n-1) - a(n-3) + a(n-4) for n > 3. - Wesley Ivan Hurt, Jul 05 2016
a(n) = 2*floor(n/6) - floor(n/3) + 1. - Ridouane Oudra, Dec 14 2021
MAPLE
seq(op([1, 1, 1, 0, 0, 0]), n=0..40); # Wesley Ivan Hurt, Jul 05 2016
MATHEMATICA
CoefficientList[Series[(1 + x + x^2)/(1 - x^6), {x, 0, 50}], x]
Flatten[Table[{1, 1, 1, 0, 0, 0}, {20}]] (* Harvey P. Dale, Jul 17 2011 *)
PROG
(PARI) a(n)=n%6<3 \\ Jaume Oliver Lafont, Mar 17 2009
(Magma) &cat [[1, 1, 1, 0, 0, 0]^^30]; // Wesley Ivan Hurt, Jul 05 2016
(Python)
def A088911(n): return int(n % 6 < 3) # Chai Wah Wu, May 25 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Oct 22 2003
STATUS
approved