A270825 a(n) = Sum_{i=0..n} (-1)^floor(i/2)*floor(sqrt(i)).

0, 1, 0, -1, 1, 3, 1, -1, 1, 4, 1, -2, 1, 4, 1, -2, 2, 6, 2, -2, 2, 6, 2, -2, 2, 7, 2, -3, 2, 7, 2, -3, 2, 7, 2, -3, 3, 9, 3, -3, 3, 9, 3, -3, 3, 9, 3, -3, 3, 10, 3, -4, 3, 10, 3, -4, 3, 10, 3, -4, 3, 10, 3, -4, 4, 12, 4, -4, 4, 12, 4, -4, 4, 12, 4, -4, 4

Offset

0,6

Links

Table of n, a(n) for n=0..76.

Formula

a(4m)=floor(sqrt(m)), a(4m+1)=floor(3/2*floor(sqrt(4m+1))), a(4m+2)=floor(sqrt(m)), a(4m+3)=-floor((1+sqrt(4m+3))/2).

Example

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

Mathematica

Print[Table[Sum[(-1)^(Floor[i/2])*Floor[Sqrt[i]], {i, 0, n}], {n, 0, 100}]]

Prog

(PARI) a(n)=sum(i=0, n, (-1)^(floor(i/2))*floor(sqrt(i)))

Crossrefs

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

Sequence in context: A318577 A157603 A305439 * A364096 A348028 A059619

Adjacent sequences: A270822 A270823 A270824 * A270826 A270827 A270828

Keyword

sign,easy

Author

John M. Campbell, Mar 23 2016

Status

approved