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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.
4
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.
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
KEYWORD
nonn
AUTHOR
Kirill Ustyantsev, Apr 27 2018
STATUS
approved