A237526 a(n) = number of unit squares in the first quadrant of a disk of radius sqrt(n) centered at the origin of a square lattice.

0, 0, 1, 1, 1, 3, 3, 3, 4, 4, 6, 6, 6, 8, 8, 8, 8, 10, 11, 11, 13, 13, 13, 13, 13, 15, 17, 17, 17, 19, 19, 19, 20, 20, 22, 22, 22, 24, 24, 24, 26, 28, 28, 28, 28, 30, 30, 30, 30, 30, 33, 33, 35, 37, 37, 37, 37, 37, 39, 39, 39, 41, 41, 41, 41, 45, 45, 45, 47, 47

Offset

0,6

Links

Table of n, a(n) for n=0..69.

Formula

a(A000404(n)) = A232499(n).

a(n) = Sum_{k=1..sqrt(n)} floor(sqrt(n-k^2)). - M. F. Hasler, Feb 09 2014

G.f.: (theta_3(x) - 1)^2/(4*(1 - x)), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 17 2018

Prog

(PARI) A237526(n)=sum(k=1, sqrtint(n), sqrtint(n-k^2)) \\ M. F. Hasler, Feb 09 2014

Crossrefs

Cf. A000404, A001481, A057961, A232499.

Partial sums of A063725.

Sequence in context: A120204 A177018 A156349 * A240117 A333536 A069941

Adjacent sequences: A237523 A237524 A237525 * A237527 A237528 A237529

Keyword

nonn

Author

L. Edson Jeffery, Feb 09 2014

Status

approved