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A270370 a(n) = Sum_{k=0..n} (-1)^k*floor(k^(1/3)). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A134451 A229217 A167965 * A167966 A167967 A160990

Adjacent sequences:  A270367 A270368 A270369 * A270371 A270372 A270373

KEYWORD

sign,easy

AUTHOR

John M. Campbell, Mar 15 2016

STATUS

approved

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Last modified September 16 12:57 EDT 2019. Contains 327113 sequences. (Running on oeis4.)