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A080425
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Jacobsthal selector sequence.
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12
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0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1
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OFFSET
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0,2
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COMMENTS
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The Jacobsthal sequence A001045 can be defined by A001045(n)=Sum{k=0..floor(n,3), binomial(n, A080425(n-1)+3k)}
a(n) = A130196(n) + A131534(n) - 2. [From Reinhard Zumkeller, Nov 12 2009]
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LINKS
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Table of n, a(n) for n=0..104.
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FORMULA
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a(n)=ceiling((mod(n, 3)+1)/2)+(-1)^(mod(n, 3)+1)
G.f.: x(x+2)/(1-x^3) - Paul Barry, May 25 2003
a(n) = (3 - n mod 3) mod 3. - Reinhard Zumkeller, Jul 30 2005
a(n)=2*A001045(L(n/3)), where L(j/p) is the Legendre symbol of j and p.
a(n)=(-n) mod 3; also a(n)=3*ceiling(n/3)-n. - Hieronymus Fischer, May 29 2007
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MAPLE
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[seq (modp((2*n+1), 3), n=1..90)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2006
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PROG
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(Haskell)
a080425 = (`mod` 3) . (3 -) . (`mod` 3)
a080425_list = cycle [0, 2, 1] -- Reinhard Zumkeller, Feb 22 2013
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CROSSREFS
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Cf. A001045, A007318.
Cf. A010872.
Sequence in context: A112203 A196279 A132798 * A048141 A025664 A025854
Adjacent sequences: A080422 A080423 A080424 * A080426 A080427 A080428
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Feb 20 2003
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EXTENSIONS
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More terms from Reinhard Zumkeller, Jul 30 2005
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STATUS
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approved
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