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

1,3

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

Table of n, a(n) for n=1..53.

Kirill Ustyantsev, Desmos graph calculator

Formula

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

Prog

(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*y<n*n and x+y>n):
....count=count+1
.print(4*count)
(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

Crossrefs

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

Sequence in context: A335992 A233341 A102110 * A055079 A081833 A370134

Adjacent sequences: A302826 A302827 A302828 * A302830 A302831 A302832

Keyword

nonn

Author

Kirill Ustyantsev, Apr 27 2018

Status

approved