A303642
a(n) is the number of lattice points in Cartesian grid between circle of radius n and its inscribed square. The sides of the square are parallel to coordinate axes.
Original entry on oeis.org
0, 0, 0, 20, 20, 28, 64, 72, 80, 80, 148, 148, 156, 248, 256, 264, 264, 380, 396, 404, 528, 552, 560, 700, 716, 740, 764, 928, 936, 960, 1148, 1180, 1196, 1212, 1440, 1448, 1472, 1700, 1740, 1764, 2000, 2040, 2064, 2104, 2380, 2396, 2428, 2720, 2760, 2784, 2832, 3156
Offset: 1
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import math
for n in range(1, 100):
count = 0
for x in range(0, n):
for y in range(-n, n):
if (x * x + y * y < n * n and x > n / math.sqrt(2)):
count = count + 1
print(4 * count)
A303644
a(n) is the number of lattice points in a Cartesian grid between a square of side length 2*n, centered at the origin, and its inscribed circle. The sides of the square are parallel to the coordinate axes.
Original entry on oeis.org
0, 0, 0, 4, 4, 12, 24, 32, 40, 48, 68, 92, 100, 120, 136, 168, 192, 220, 244, 268, 312, 336, 376, 420, 444, 484, 524, 576, 624, 664, 724, 764, 820, 868, 912, 992, 1040, 1116, 1156, 1220, 1304, 1368, 1440, 1496, 1564, 1660, 1732, 1816, 1888, 1960, 2032, 2116, 2220, 2308
Offset: 1
For n = 4, we have 4 points with integer coordinates; the point in the first quadrant is at (3,3):
.
o . . + . . o
. . . + . . .
. . . + . . .
-+-+-+-+-+-+-+-
. . . + . . .
. . . + . . .
o . . + . . o
.
Similarly, for n = 5, we have 4 points with integer coordinates; the point in the first quadrant is at (4,4):
.
o . . . + . . . o
. . . . + . . . .
. . . . + . . . .
. . . . + . . . .
-+-+-+-+-+-+-+-+-+-
. . . . + . . . .
. . . . + . . . .
. . . . + . . . .
o . . . + . . . o
.
For n = 6, we have 12 points, of which the 3 points in the first quadrant are at (4,5), (5,4), and (5,5):
.
o o . . . + . . . o o
o . . . . + . . . . o
. . . . . + . . . . .
. . . . . + . . . . .
. . . . . + . . . . .
-+-+-+-+-+-+-+-+-+-+-+-
. . . . . + . . . . .
. . . . . + . . . . .
. . . . . + . . . . .
o . . . . + . . . . o
o o . . . + . . . o o
-
a(n) = sum(x=-n+1, n-1, sum(y=-n+1, n-1, (x^2+y^2) > n^2)); \\ Michel Marcus, May 22 2018
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import math
for n in range(1, 100):
count = 0
for x in range(1, n):
for y in range(1, n):
if x * x + y * y > n * n and x < n and y < n:
count = count + 1
print(4 * count, end=", ")
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.
Original entry on oeis.org
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
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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
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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)
A303669
a(n) is the number of lattice points in a Cartesian grid between a circle of radius n, centered at the origin, and an inscribed equilateral triangle; one of the sides of triangle is perpendicular to X-axis.
Original entry on oeis.org
0, 2, 13, 21, 36, 56, 81, 103, 144, 166, 215, 239, 298, 342, 405, 447, 514, 568, 655, 707, 796, 864, 961, 1019, 1128, 1208, 1337, 1405, 1524, 1614, 1749, 1847, 1990, 2082, 2249, 2333, 2502, 2600, 2789, 2899, 3064, 3192, 3383, 3519, 3718, 3832, 4047, 4175
Offset: 1
For n = 2 we have two lattice points between the defined circle and its inscribed equilateral triangle: (1, 1) and (1, -1).
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a(n) = sum(x=-n, +n, sum(y=-n, +n, ((x^2+y^2) < n^2) && ((2*x < - n) || (3*y^2 > (n-x)^2)))); \\ Michel Marcus, May 22 2018
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import math
tan=math.sqrt(3)/3
for n in range (1,70):
count=0
count1=0
for x in range (-n, n):
for y in range (-n,n):
if (x*x+y*y-tan*x+tan*n):
count=count+1
if (x*x+y*y
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