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A103368
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Period 6: repeat 1,1,-1,-1,0,0.
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1
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1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0, 1, 1, -1, -1, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| G.f.: (1+x)/(1+x^2+x^4).
The positive sequence is A131719(n+1) = a(n)=(cos(2*pi*n/3+pi/3)/6+sqrt(3)sin(2*pi*n/3+pi/3)/6 -sqrt(3)cos(pi*n/3+pi/6)/6+sin(pi*n/3+pi/6)/2+2/3, with g.f. (-1-x^2) / ( (x-1)*(1-x+x^2)*(1+x+x^2) ).
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FORMULA
| a(n)=sum{k=0..floor(n/2), binomial(k, floor(n/2)-k)(-1)^k); a(n)=-cos(2*pi*n/3+pi/3)/2+sqrt(3)sin(2*pi*n/3+pi/3)/6+sqrt(3)cos(pi*n/3+pi/6)/2+sin(pi*n/3+pi/6)/2.
a(n) = cos(Pi*n/3) +sin(2*Pi*n/3)/sqrt(3). - R. J. Mathar, Oct 08 2011
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CROSSREFS
| Sequence in context: A084846 A130093 A166446 * A055132 A128408 A121802
Adjacent sequences: A103365 A103366 A103367 * A103369 A103370 A103371
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 02 2005
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