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A088911
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Period 6: repeat 1,1,1,0,0,0.
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15
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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; internal format)
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OFFSET
| 0,1
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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 (gdetlefs(AT)aol.com), May 17 2011]
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LINKS
| Index entries for sequences related to Chebyshev polynomials.
Index to sequences with linear recurrences with constant coefficients, signature (1,0,-1,1).
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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.
a(n)=sum(k=0..floor(n/2), U(n-2k, 1/2) ) - Paul Barry (pbarry(AT)wit.ie), 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 (pbarry(AT)wit.ie), Mar 14 2004
a(n)= floor(((n+3) mod 6)/3)
a(n)= floor((5*n-1)/3) mod 2. [From Gary Detlefs (gdetlefs(AT)aol.com), 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
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MATHEMATICA
| CoefficientList[Series[(1 + x + x^2)/(1 - x^6), {x, 0, 50}], x]
Flatten[Table[{1, 1, 1, 0, 0, 0}, {20}]] (* From Harvey P. Dale, Jul 17 2011 *)
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PROG
| (PARI) a(n)=n%6<3 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 17 2009]
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CROSSREFS
| Cf. A000035, A133872, A131078, A112713.
Sequence in context: A143466 A117908 A115360 * A179763 A105349 A096606
Adjacent sequences: A088908 A088909 A088910 * A088912 A088913 A088914
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KEYWORD
| base,nonn,easy
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Oct 22 2003
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EXTENSIONS
| More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net) and Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 24 2003
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