

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
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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+111+2+222 = 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



