A362233 -id:A362233 - cp's OEIS frontend

A373106 Number of vertices among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4n points placed on the sides of a square when every pair of the 4 + 4n points are connected by a circle and where the points lie at the ends of the circle's diameter.

5, 61, 677, 2533, 7705, 17269, 37161, 65089, 111877, 174545, 274213

Offset: 0

Scott R. Shannon, May 25 2024

A circle is constructed for every pair of the 4 + 4*n points, the two points lying at the ends of a diameter of the circle.

Scott R. Shannon, Image for n = 0. In this and other images the 4 + 4*n vertices forming the square are drawn larger for clarity.
Scott R. Shannon, Image for n = 1.
Scott R. Shannon, Image for n = 2.
Scott R. Shannon, Image for n = 3.

Cf. A373107 (regions), A373108 (edges), A373109 (k-gons), A373110 (circles), A372977, A372731, A358746, A362233, A360351.

a(n) = A373108(n) - A373107(n) + 1 by Euler's formula.

A362234 Number of regions among all distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes when each pair of points is connected by a circle and where the points lie at the ends of the circles' diameter.

Original entry on oeis.org

32, 372, 1804, 5772, 14660, 30816, 58232, 100080, 161700, 249200, 368384

Offset: 1

Scott R. Shannon, Apr 13 2023

A circle is constructed for every pair of the 1 + 4n points, the two points lying at the ends of a diameter of the circle. The number of distinct circles constructed from the points is A139275(n).

No formula for a(n) is currently known.

Scott R. Shannon, Image for n = 1.
Scott R. Shannon, Image for n = 2.
Scott R. Shannon, Image for n = 3.
Scott R. Shannon, Image for n = 4.

Cf. A362233 (vertices), A362235 (edges), A362236 (k-gons), A139275 (distinct circles), A353782, A359933.

a(n) = A362235(n) - A362233(n) + 1 by Euler's formula.

A362235 Number of edges among all distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes when each pair of points is connected by a circle and where the points lie at the ends of the circles' diameter.

Original entry on oeis.org

48, 620, 3184, 10516, 27240, 57676, 109880, 189436, 307200, 474820, 703880

Offset: 1

Scott R. Shannon, Apr 13 2023

A circle is constructed for every pair of the 1 + 4n points, the two points lying at the ends of a diameter of the circle. The number of distinct circles constructed from the points is A139275(n).
No formula for a(n) is currently known.
See A362233 and A362234 for images of the circles.

Cf. A362233 (vertices), A362234 (regions), A362236 (k-gons), A139275 (distinct circles), A356358, A359934.

a(n) = A362234(n) + A362233(n) - 1 by Euler's formula.

A362236 Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, among all distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes when each pair of points is connected by a circle and where the points lie at the ends of the circles' diameter.

Original entry on oeis.org

12, 12, 8, 32, 204, 120, 16, 56, 928, 652, 156, 4, 8, 72, 2724, 2332, 504, 120, 16, 4, 96, 6416, 6120, 1648, 352, 20, 8, 128, 13356, 12444, 4156, 668, 52, 12, 208, 24348, 23892, 8148, 1488, 124, 24, 248, 41268, 41528, 14108, 2616, 276, 36, 336, 65684, 67272, 23372, 4592, 388, 52, 0, 4

Offset: 1

Scott R. Shannon, Apr 13 2023

A circle is constructed for every pair of the 1 + 4n points, the two points lying at the ends of a diameter of the circle. The number of distinct circles constructed from the points is A139275(n).

See A362233 and A362234 for images of the circles.

			The table begins:
 12, 12, 8;
 32, 204, 120, 16;
 56, 928, 652, 156, 4, 8;
 72, 2724, 2332, 504, 120, 16, 4;
 96, 6416, 6120, 1648, 352, 20, 8;
 128, 13356, 12444, 4156, 668, 52, 12;
 208, 24348, 23892, 8148, 1488, 124, 24;
 248, 41268, 41528, 14108, 2616, 276, 36;
 336, 65684, 67272, 23372, 4592, 388, 52, 0, 4;
 384, 99440, 105260, 36028, 7316, 708, 60, 4;
 464, 144684, 156976, 54136, 10792, 1224, 100, 8;
 .
 .

Cf. A362233 (vertices), A362234 (regions), A362235 (edges), A139275 (distinct circles), A361623, A359935.

Sum of row n = A362234(n).

cp's OEIS Frontend

A373106 Number of vertices among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4n points placed on the sides of a square when every pair of the 4 + 4n points are connected by a circle and where the points lie at the ends of the circle's diameter.

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A362234 Number of regions among all distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes when each pair of points is connected by a circle and where the points lie at the ends of the circles' diameter.

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A362235 Number of edges among all distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes when each pair of points is connected by a circle and where the points lie at the ends of the circles' diameter.

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cp's OEIS Frontend

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.

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A362234 Number of regions among all distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes when each pair of points is connected by a circle and where the points lie at the ends of the circles' diameter.

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A362235 Number of edges among all distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes when each pair of points is connected by a circle and where the points lie at the ends of the circles' diameter.

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A373106 Number of vertices among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4n points placed on the sides of a square when every pair of the 4 + 4n points are connected by a circle and where the points lie at the ends of the circle's diameter.