A372978
Number of regions among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square, using only a compass.
Original entry on oeis.org
45, 628, 4633, 15476, 41561, 98808, 206317, 333272, 590181
Offset: 0
A372981
Number of distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square, using only a compass.
Original entry on oeis.org
8, 32, 88, 160, 264, 400, 576, 732, 968, 1184, 1480, 1728, 2104, 2424, 2840, 3196, 3688, 4088, 4640, 5048, 5704, 6248, 6904, 7364
Offset: 0
A373106
Number of vertices among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square when every pair of the 4 + 4*n points are connected by a circle and where the points lie at the ends of the circle's diameter.
Original entry on oeis.org
5, 61, 677, 2533, 7705, 17269, 37161, 65089, 111877, 174545, 274213
Offset: 0
A372979
Number of edges among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square, using only a compass.
Original entry on oeis.org
84, 1180, 8836, 29980, 80564, 193172, 403780, 654196, 1159780
Offset: 0
A372980
Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square, using only a compass.
Original entry on oeis.org
16, 29, 272, 260, 80, 12, 4, 1708, 2253, 528, 120, 20, 4, 5200, 7636, 2136, 432, 44, 20, 8, 13732, 20788, 5712, 1120, 184, 17, 8, 31576, 49284, 14060, 3180, 584, 108, 16, 64748, 103557, 30372, 6472, 980, 172, 4, 12, 103368, 166804, 49920, 11196, 1660, 260, 48, 16, 181376, 296388, 88916, 19844, 3128, 445, 64, 20
Offset: 0
The table begins:
16, 29;
272, 260, 80, 12, 4;
1708, 2253, 528, 120, 20, 4;
5200, 7636, 2136, 432, 44, 20, 8;
13732, 20788, 5712, 1120, 184, 17, 8;
31576, 49284, 14060, 3180, 584, 108, 16;
64748, 103557, 30372, 6472, 980, 172, 4, 12;
103368, 166804, 49920, 11196, 1660, 260, 48, 16;
181376, 296388, 88916, 19844, 3128, 445, 64, 20;
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A385161
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 (finite) regions created.
Original entry on oeis.org
1, 117, 4713, 41173, 233365, 725081, 2323869
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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