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

1,3

Comments

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

Links

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

Kirill Ustyantsev, Graphic illustration

Prog

(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)<n*math.sqrt(2)):
               count += 1
   print(count)
(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

Crossrefs

Cf. A302829, A303642, A303644.

Sequence in context: A070710 A048759 A364434 * A298036 A119877 A307842

Adjacent sequences: A303643 A303644 A303645 * A303647 A303648 A303649

Keyword

nonn

Author

Kirill Ustyantsev, Apr 27 2018

Status

approved