A303646 a(n) is the number of lattice points in a Cartesian grid between a square with integer sides 2*n and its inscribed circle. The sides of the square are parallel to the bisector of coordinate axes.

0, 0, 12, 12, 32, 32, 32, 68, 60, 104, 104, 104, 156, 148, 216, 216, 300, 292, 276, 368, 368, 468, 460, 452, 560, 544, 676, 668, 816, 792, 784, 932, 916, 1080, 1048, 1048, 1220, 1212, 1384, 1360, 1352, 1556, 1532, 1736, 1704, 1956, 1924, 1900, 2136, 2096, 2340, 2308

Offset: 1

Author

Kirill Ustyantsev, Apr 27 2018

Keywords

• nonn

Comments

Rotating the square by 45 degrees (so that its vertices lie on the coordinate axes) results in sequence A303644 instead.

Links

• Kirill Ustyantsev, Graphic illustration

Crossrefs

Cf. A302829, A303642, A303644.

Programs

PARI

a(n) = sum(x=-2*n, 2*n, sum(y=-2*n, 2*n, ((x^2+y^2) > n^2) && ((abs(x)+abs(y))^2 < 2*n^2))); \\ Michel Marcus, May 22 2018

Python

import math
for n in range (1, 100):
   sqn = math.ceil(math.sqrt(2)*n)
   count = 0
   for x in range(-sqn, sqn):
       for y in range(-sqn, sqn):
           if (x*x+y*y>n*n and abs(x)+abs(y)