cp's OEIS Frontend

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.

%I A303646 #23 Jun 09 2020 09:28:44
%S A303646 0,0,12,12,32,32,32,68,60,104,104,104,156,148,216,216,300,292,276,368,
%T A303646 368,468,460,452,560,544,676,668,816,792,784,932,916,1080,1048,1048,
%U A303646 1220,1212,1384,1360,1352,1556,1532,1736,1704,1956,1924,1900,2136,2096,2340,2308
%N 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.
%C A303646 Rotating the square by 45 degrees (so that its vertices lie on the coordinate axes) results in sequence A303644 instead.
%H A303646 Kirill Ustyantsev, <a href="https://www.desmos.com/calculator/esxgfyvpj3">Graphic illustration</a>
%o A303646 (Python)
%o A303646 import math
%o A303646 for n in range (1, 100):
%o A303646    sqn = math.ceil(math.sqrt(2)*n)
%o A303646    count = 0
%o A303646    for x in range(-sqn, sqn):
%o A303646        for y in range(-sqn, sqn):
%o A303646            if (x*x+y*y>n*n and abs(x)+abs(y)<n*math.sqrt(2)):
%o A303646                count += 1
%o A303646    print(count)
%o A303646 (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
%Y A303646 Cf. A302829, A303642, A303644.
%K A303646 nonn
%O A303646 1,3
%A A303646 _Kirill Ustyantsev_, Apr 27 2018