A302829 a(n) is the number of lattice points in a Cartesian grid between a circle of radius n and an inscribed square whose vertices lie on the coordinate axes.

0, 0, 4, 8, 12, 28, 36, 52, 72, 88, 112, 128, 156, 192, 220, 252, 280, 324, 368, 408, 448, 504, 548, 592, 644, 708, 776, 828, 880, 952, 1016, 1096, 1164, 1236, 1324, 1388, 1472, 1548, 1648, 1736, 1808, 1912, 2004, 2116, 2212, 2300, 2408, 2508, 2624, 2728, 2860, 2976, 3076

Offset: 1

Author

Kirill Ustyantsev, Apr 27 2018

Keywords

• nonn

Comments

Points are not lying on the borders of the circle and the square.

Note that if the square is rotated so that its sides are parallel to the coordinate axes, the resulting sequence is A303642 instead.

Links

• Kirill Ustyantsev, Desmos graph calculator

Crossrefs

Cf. A034856, A281795, A303642, A303644, A303646.

Programs

PARI

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

Python

for n in range (1, 100):
    count=0
    for x in range (0, n):
        for y in range (0, n):
            if (x*x+y*yn):
                count=count+1
    print(4*count)

Formula

a(n) = A281795(n) - 4*A034856(n). - Andrey Zabolotskiy, Apr 29 2018