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A281795
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Number of unit squares (partially) covered by a disk of radius n centered at the origin.
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2
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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
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0,2
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COMMENTS
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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 bottom-left corner.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n-1} 4*ceiling(sqrt(n^2-k^2)). - Luis Mendo, Aug 09 2021
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EXAMPLE
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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.
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PROG
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(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:n-1).^2))); % Luis Mendo, Aug 09 2021
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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