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a(n) is the number of lattice points in Cartesian grid between circle of radius n and its inscribed square. The sides of the square are parallel to coordinate axes.
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%I #22 May 05 2018 19:44:45

%S 0,0,0,20,20,28,64,72,80,80,148,148,156,248,256,264,264,380,396,404,

%T 528,552,560,700,716,740,764,928,936,960,1148,1180,1196,1212,1440,

%U 1448,1472,1700,1740,1764,2000,2040,2064,2104,2380,2396,2428,2720,2760,2784,2832,3156

%N a(n) is the number of lattice points in Cartesian grid between circle of radius n and its inscribed square. The sides of the square are parallel to coordinate axes.

%C If the sides of the inscribed square are parallel to bisector of coordinate axes we have a different sequence.

%H Kirill Ustyantsev, <a href="https://www.desmos.com/calculator/ravtawi4o9">illustrated example</a>

%o (Python)

%o import math

%o for n in range(1, 100):

%o .count = 0

%o .for x in range(0, n):

%o ..for y in range(-n, n):

%o ...if (x * x + y * y < n * n and x > n / math.sqrt(2)):

%o ....count = count + 1

%o .print(4 * count)

%Y Cf. A302829, A303644, A303646.

%K nonn

%O 1,4

%A _Kirill Ustyantsev_, Apr 27 2018

%E Offset corrected by _Andrey Zabolotskiy_, May 05 2018