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A303642 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.

%I A303642 #24 May 22 2025 10:21:47
%S A303642 0,0,0,20,20,28,64,72,80,80,148,148,156,248,256,264,264,380,396,404,
%T A303642 528,552,560,700,716,740,764,928,936,960,1148,1180,1196,1212,1440,
%U A303642 1448,1472,1700,1740,1764,2000,2040,2064,2104,2380,2396,2428,2720,2760,2784,2832,3156
%N A303642 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 A303642 If the sides of the inscribed square are parallel to bisector of coordinate axes we have a different sequence.
%H A303642 Kirill Ustyantsev, <a href="https://www.desmos.com/calculator/ravtawi4o9">illustrated example</a>
%o A303642 (Python)
%o A303642 import math
%o A303642 for n in range(1, 100):
%o A303642  count = 0
%o A303642  for x in range(0, n):
%o A303642   for y in range(-n, n):
%o A303642    if (x * x + y * y < n * n and x > n / math.sqrt(2)):
%o A303642     count = count + 1
%o A303642  print(4 * count)
%Y A303642 Cf. A302829, A303644, A303646.
%K A303642 nonn
%O A303642 1,4
%A A303642 _Kirill Ustyantsev_, Apr 27 2018
%E A303642 Offset corrected by _Andrey Zabolotskiy_, May 05 2018