

A281795


Number of unit squares (partially) covered by a disk of radius n centered at the origin.


2



0, 4, 16, 36, 60, 88, 132, 172, 224, 284, 344, 416, 484, 568, 664, 756, 856, 956, 1076, 1200, 1324, 1452, 1600, 1740, 1884, 2040, 2212, 2392, 2560, 2732, 2928, 3120, 3332, 3536, 3748, 3980, 4192, 4428, 4660, 4920, 5172, 5412, 5688, 5956, 6248, 6528, 6804, 7104, 7400, 7716
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OFFSET

0,2


COMMENTS

Touching a unit square does not count as covering. E.g., the disk with radius 5 does not cover the unit square with (3, 4) as bottomleft corner.


LINKS

Table of n, a(n) for n=0..49.


FORMULA

a(n) = 4*A001182(n) + A242118(n).  Andrey Zabolotskiy, Jan 30 2017
a(n) = Sum_{k=0..n1} 4*ceiling(sqrt(n^2k^2)).  Luis Mendo, Aug 09 2021


EXAMPLE

a(4) = 4 * 15 = 60 because in the positive quadrant 15 unit squares are covered and the problem is symmetrical. In the bounding box of the circle only the unit squares in the corners are not (partially) covered, so a(4) = 8*8  4 = 60.


PROG

(Python)
a = lambda n: sum(4 for x in range(n) for y in range(n)
if x*x + y*y < n*n)
(Matlab / Octave)
a = @(n) 4*sum(ceil(sqrt(n.^2(0:n1).^2))); % Luis Mendo, Aug 09 2021


CROSSREFS

Cf. A001182, A242118.
Sequence in context: A014727 A174597 A044065 * A063540 A349223 A055808
Adjacent sequences: A281792 A281793 A281794 * A281796 A281797 A281798


KEYWORD

nonn,easy


AUTHOR

Orson R. L. Peters, Jan 30 2017


STATUS

approved



