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A088911 Period 6: repeat 1,1,1,0,0,0. 15
1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
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). [From Gary Detlefs, May 17 2011]

LINKS

Table of n, a(n) for n=0..104.

Index entries for sequences related to Chebyshev polynomials.

Index to sequences with linear recurrences with constant coefficients, signature (1,0,-1,1).

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

Partial sums of expansion of 1/(1+x^3), see A131531. a(n)=2*sin(pi*r/3+pi/6)/3+cos(pi*r)/6+1/2 - Paul Barry, Mar 14 2004

a(n)= floor(((n+3) mod 6)/3)

a(n)= floor((5*n-1)/3) mod 2. [From 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]

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

CROSSREFS

Cf. A000035, A133872, A131078, A112713.

Sequence in context: A143466 A117908 A115360 * A179763 A105349 A096606

Adjacent sequences:  A088908 A088909 A088910 * A088912 A088913 A088914

KEYWORD

nonn,base,easy

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Oct 22 2003

EXTENSIONS

More terms from Ray Chandler and Robert G. Wilson v, Oct 24 2003

STATUS

approved

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Last modified August 30 14:36 EDT 2014. Contains 246224 sequences.