A374826
Place n equally spaced points on the circumference of a circle of radius r and then connect each pair of points with straight lines whose intersections create A007569(n) - n additional points. Draw a circle of radius r around each of the A007569(n) points. The sequence gives the total number of regions formed from all circle intersections.
Original entry on oeis.org
1, 2, 6, 16, 80, 324, 1666, 3120, 17703, 28780, 115401, 96624, 528073, 589708
Offset: 1
A374827
Place n equally spaced points on the circumference of a circle of radius r and then connect each pair of points with straight lines whose intersections create A007569(n) - n additional points. Draw a circle of radius r around each of the A007569(n) points. The sequence gives the total number of curved edges formed from all circle intersections.
Original entry on oeis.org
1, 2, 9, 28, 150, 636, 3290, 6192, 35145, 57380, 230494, 192588, 1055535, 1177148
Offset: 1
A374828
Irregular table read by rows: Place n equally spaced points on the circumference of a circle of radius r and then connect each pair of points with straight lines whose intersections create A007569(n) - n additional points. Draw a circle of radius r around each of the A007569(n) points. T(n,k) is the number of k-sided regions, k>=2, formed from all circle intersections.
Original entry on oeis.org
3, 3, 0, 12, 4, 5, 45, 10, 10, 10, 0, 156, 84, 48, 30, 6, 0, 742, 476, 294, 119, 21, 14, 0, 1104, 1296, 512, 152, 40, 16, 0, 6669, 6768, 2790, 1179, 207, 81, 9, 0, 10280, 11130, 5490, 1440, 260, 150, 20, 10, 0, 40777, 45342, 20669, 6963, 1177, 374, 77, 11, 11
Offset: 3
The table begins:
3, 3;
0, 12, 4;
5, 45, 10, 10, 10;
0, 156, 84, 48, 30, 6;
0, 742, 476, 294, 119, 21, 14;
0, 1104, 1296, 512, 152, 40, 16;
0, 6669, 6768, 2790, 1179, 207, 81, 9;
0, 10280, 11130, 5490, 1440, 260, 150, 20, 10;
0, 40777, 45342, 20669, 6963, 1177, 374, 77, 11, 11;
0, 33672, 39552, 16236, 5772, 1080, 288, 0, 12, 0, 12;
0, 181467, 212186, 97461, 30082, 5252, 1430, 78, 104, 0, 0, 13;
0, 198772, 246134, 104356, 33348, 5614, 1190, 252, 28, 0, 0, 0, 14;
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A384701
On a 2 X n grid of vertices, draw a circle through every unordered triple of non-collinear vertices: a(n) is the number of distinct points where circles intersect.
Original entry on oeis.org
2, 4, 18, 172, 978, 3672, 11034, 27241, 60804, 122741, 232138, 412263, 697058
Offset: 1
A385160
Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join a circle through every unordered triple of non-collinear points: a(n) is the number of distinct points where circles intersect.
Original entry on oeis.org
4, 68, 4244, 38100, 222300, 695544, 2252764
Offset: 1
- Scott R. Shannon, Image for n = 2. The 4 x 2 = 8 starting points are shown as white dots.
- Scott R. Shannon, Image for n = 3. The 4 x 3 = 12 starting points are shown as white dots.
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