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A270825 a(n) = Sum_{i=0..n} (-1)^floor(i/2)*floor(sqrt(i)). 0
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 (list; graph; refs; listen; history; text; internal format)
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 * A059619 A098950 A318873

Adjacent sequences:  A270822 A270823 A270824 * A270826 A270827 A270828

KEYWORD

sign,easy

AUTHOR

John M. Campbell, Mar 23 2016

STATUS

approved

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Last modified December 13 12:37 EST 2019. Contains 329968 sequences. (Running on oeis4.)