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A270370
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a(n) = Sum_{k=0..n} (-1)^k*floor(k^(1/3)).
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2
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0, -1, 0, -1, 0, -1, 0, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 2, -2, 2, -2, 2, -2
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OFFSET
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0,28
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LINKS
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FORMULA
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a(n) = floor(n^(1/3))*(-1)^n/2 - ((-1)^(floor(n^(1/3))+1)+1)/4.
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EXAMPLE
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a(5) = [0^(1/3)]-[1^(1/3)]+[2^(1/3)]-[3^(1/3)]+[4^(1/3)]-[5^(1/3)] = 0-1+1-1+1-1 = -1, letting [] denote the floor function.
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MATHEMATICA
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Print[Table[Sum[(-1)^i*Floor[i^(1/3)], {i, 0, n}], {n, 0, 100}]]
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PROG
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(PARI) a(n)=sum(i=0, n, (-1)^i*sqrtnint(i, 3))
(PARI) a(n)=sqrtnint(n, 3)*(-1)^n/2-((-1)^(sqrtnint(n, 3)+1)+1)/4
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CROSSREFS
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Cf. A268173, A022554, A031876, A032512, A032513, A032514, A032515, A032516, A032517, A032518, A032519, A032520, A032521.
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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