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A088911 Period 6: repeat [1, 1, 1, 0, 0, 0]. 17
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). [Gary Detlefs, May 17 2011]

LINKS

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

Index entries for sequences related to Chebyshev polynomials.

Index entries for 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

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) = A079979(n)+A079979(n-1)+A079979(n-2). - R. J. Mathar, Jul 10 2015

a(n) = a(n-1) - a(n-3) + a(n-4) for n>3. - Wesley Ivan Hurt, Jul 05 2016

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

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,easy

AUTHOR

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

STATUS

approved

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Last modified July 27 18:57 EDT 2016. Contains 275102 sequences.