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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

L. Edson Jeffery, Feb 09 2014

STATUS

approved

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Last modified July 7 12:08 EDT 2022. Contains 355148 sequences. (Running on oeis4.)