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A101675
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G.f.: (1-x-x^2)/(1+x^2+x^4).
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3
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1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2, 1, 1, 0, 1, -1, -2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 04 2008: (Start)
The sequence has a 12 term periodic cycle if indexed with offset 1, starting:
(1, 1, 0, -1, -1, -2, -1, -1, 0, 1, 1, 2,...(repeat)); such that even terms =
2*Cos(n*Pi/6) and odds = (2/(sqrt3))*Cos(n*Pi/6). (End)
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(0) = 1, a(1) = -1, a(2) = -2, a(3) = 1; for n >= 4, a(n)=-a(n-2)-a(n-4).
a(n)=sum{k=0..floor(n/2), (-1)^A010060(n-2k)*mod(binomial(n-k, k), 2)(-1)^k}; a(n)=cos(2*pi*n/3+pi/6)/sqrt(3)+sin(2*pi*n/3+pi/6)+cos(pi*n/3+pi/3)-sin(pi*n/3+pi/3)/sqrt(3).
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CROSSREFS
| Partial sums are A101676.
Sequence in context: A037906 A120936 A173432 * A051764 A025906 A020944
Adjacent sequences: A101672 A101673 A101674 * A101676 A101677 A101678
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Dec 11 2004
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