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.

0, 0, 0, 20, 20, 28, 64, 72, 80, 80, 148, 148, 156, 248, 256, 264, 264, 380, 396, 404, 528, 552, 560, 700, 716, 740, 764, 928, 936, 960, 1148, 1180, 1196, 1212, 1440, 1448, 1472, 1700, 1740, 1764, 2000, 2040, 2064, 2104, 2380, 2396, 2428, 2720, 2760, 2784, 2832, 3156

Offset: 1

Author

Kirill Ustyantsev, Apr 27 2018

Keywords

• nonn

Comments

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

Links

• Kirill Ustyantsev, illustrated example

Crossrefs

Cf. A302829, A303644, A303646.

Programs

Python

import math
for n in range(1, 100):
 count = 0
 for x in range(0, n):
  for y in range(-n, n):
   if (x * x + y * y < n * n and x > n / math.sqrt(2)):
    count = count + 1
 print(4 * count)

Extensions

Offset corrected by Andrey Zabolotskiy, May 05 2018