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A080425
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Period 3: repeat [0, 2, 1].
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20
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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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Previous name was: Jacobsthal selector sequence.
The Jacobsthal sequence A001045 can be defined by A001045(n) = Sum_{k=0..floor(n,3)} C(n, a(n-1)+3*k).
The floor of the area under the polygon connecting the lattice points: (n, a(n)) from 0..n is A001477(n), the nonnegative integers. - Wesley Ivan Hurt, Jun 16 2014
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LINKS
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FORMULA
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a(n) = ceiling(((n mod 3) + 1)/2) + (-1)^((n mod 3) + 1).
a(n) = 2 * A001045(L(n/3)), where L(j/p) is the Legendre symbol of j and p.
a(n) = a(n-3) for n>2.
a(n) = 2*sin(n*Pi/3)*(3*sin(n*Pi/3) + sqrt(3)*cos(n*Pi/3))/3. (End)
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MAPLE
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MATHEMATICA
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PROG
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(Haskell)
a080425 = (`mod` 3) . (3 -) . (`mod` 3)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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