A262352 a(n) = Sum_{k=0..n} (-1)^k*floor(k^(1/4)).

0, -1, 0, -1, 0, -1, 0, -1, 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, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -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

Offset: 0

Author

John M. Campbell, Mar 24 2016

Keywords

• sign
• easy

Examples

			Letting [] denote the floor function, a(7) = [0^(1/4)] - [1^(1/4)] + [2^(1/4)] - [3^(1/4)] + [4^(1/4)] - [5^(1/4)] + [6^(1/4)] - [7^(1/4)] = 0 - 1 + 1 - 1 + 1 - 1 + 1 - 1 = -1.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537

Crossrefs

Cf. A270370, A268173, A022554, A031876, A032512, A032513, A032514, A032515, A032516, A032517, A032518, A032519, A032520, A032521.

Programs

Mathematica

Print[Table[Sum[(-1)^k*Floor[k^(1/4)],{k,0,n}],{n,0,100}]] ;

PARI

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

PARI

a(n)=sum(k=0,n,(-1)^k*floor(k^(1/4)))

PARI

A262352(n) = sum(k=0,n,((-1)^k)*sqrtnint(k, 4)); \\ Antti Karttunen, Nov 06 2018

Formula

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

Extensions

More terms from Antti Karttunen, Nov 06 2018