A270370 a(n) = Sum_{k=0..n} (-1)^k*floor(k^(1/3)).

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

Offset

0,28

Links

Table of n, a(n) for n=0..69.

Formula

a(n) = floor(n^(1/3))*(-1)^n/2 - ((-1)^(floor(n^(1/3))+1)+1)/4.

Example

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.

Mathematica

Print[Table[Sum[(-1)^i*Floor[i^(1/3)], {i, 0, n}], {n, 0, 100}]]

Prog

(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

Crossrefs

Cf. A268173, A022554, A031876, A032512, A032513, A032514, A032515, A032516, A032517, A032518, A032519, A032520, A032521.

Sequence in context: A229217 A347526 A167965 * A167966 A348998 A167967

Adjacent sequences: A270367 A270368 A270369 * A270371 A270372 A270373

Keyword

sign,easy

Author

John M. Campbell, Mar 15 2016

Status

approved