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A281795 Number of unit squares (partially) covered by a disk of radius n centered at the origin. 2

%I #18 Aug 23 2021 15:59:33

%S 0,4,16,36,60,88,132,172,224,284,344,416,484,568,664,756,856,956,1076,

%T 1200,1324,1452,1600,1740,1884,2040,2212,2392,2560,2732,2928,3120,

%U 3332,3536,3748,3980,4192,4428,4660,4920,5172,5412,5688,5956,6248,6528,6804,7104,7400,7716

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

%C 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.

%F a(n) = 4*A001182(n) + A242118(n). - _Andrey Zabolotskiy_, Jan 30 2017

%F a(n) = Sum_{k=0..n-1} 4*ceiling(sqrt(n^2-k^2)). - _Luis Mendo_, Aug 09 2021

%e 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.

%o (Python)

%o a = lambda n: sum(4 for x in range(n) for y in range(n)

%o if x*x + y*y < n*n)

%o (Matlab / Octave)

%o a = @(n) 4*sum(ceil(sqrt(n.^2-(0:n-1).^2))); % _Luis Mendo_, Aug 09 2021

%Y Cf. A001182, A242118.

%K nonn,easy

%O 0,2

%A _Orson R. L. Peters_, Jan 30 2017

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Last modified March 28 21:57 EDT 2024. Contains 371254 sequences. (Running on oeis4.)