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

1,4

Comments

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

Links

Table of n, a(n) for n=1..52.

Kirill Ustyantsev, illustrated example

Prog

(Python)
def a(n):
 count = 0
 for x in range(0, n):
  for y in range(-n, n):
   if x * x + y * y < n * n and 2 * x * x > n * n:
    count += 1
 return 4 * count
print([a(n) for n in range(1, 60)])

Crossrefs

Cf. A302829, A303644, A303646.

Sequence in context: A081245 A010859 A291522 * A278830 A040381 A354569

Adjacent sequences: A303639 A303640 A303641 * A303643 A303644 A303645

Keyword

nonn

Author

Kirill Ustyantsev, Apr 27 2018

Extensions

Offset corrected by Andrey Zabolotskiy, May 05 2018

Status

approved