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

0,82

Links

Antti Karttunen, Table of n, a(n) for n = 0..16383

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A371384 A022927 A063435 * A372584 A167964 A280193

Adjacent sequences: A262349 A262350 A262351 * A262353 A262354 A262355

Keyword

sign,easy

Author

John M. Campbell, Mar 24 2016

Extensions

More terms from Antti Karttunen, Nov 06 2018

Status

approved