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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 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 July 31 23:41 EDT 2021. Contains 346377 sequences. (Running on oeis4.)