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

Author

John M. Campbell, Mar 15 2016

Keywords

• sign
• easy

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

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

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

Formula

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