A359935 -id:A359935 - cp's OEIS frontend

A359931 Number of distinct circles that can be constructed from an n x n square grid of points using only a compass.

8, 38, 120, 277, 544, 969, 1616, 2494, 3724, 5331, 7408, 10038, 13284, 17181, 21968, 27653, 34320, 42110, 51148

Offset: 2

Scott R. Shannon, Jan 19 2023

A circle is constructed for every pair of the n x n points, the first point defines the circle's center while the second the radius distance.
No formula for a(n) is known.
See A359932 and A359933 for images of the resulting vertices and regions.

Cf. A359932 (vertices), A359933 (regions), A359934 (edges), A359935 (k-gons).

A360354 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 an n x n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle.

Original entry on oeis.org

8, 4, 40, 108, 20, 92, 904, 456, 76, 0, 8, 200, 4540, 3400, 652, 100, 4, 8, 404, 17244, 15324, 3148, 628, 116, 16, 528, 54252, 54476, 11672, 2152, 332, 44, 12, 972, 151992, 158468, 37244, 7940, 1120, 224, 48, 12, 16, 1404, 379488, 404148, 103436, 20216, 3316, 600, 132, 20, 16

Offset: 2

Scott R. Shannon, Feb 04 2023

A circle is constructed for every pair of points on the n X n grid, the points lying at the ends of a diameter of the circle.
The number of distinct circles constructed from the n x n grid is A360350(n).
See A360351 and A360352 for images of the circles.

			The table begins:
8, 4;
40, 108, 20;
92, 904, 456, 76, 0, 8;
200, 4540, 3400, 652, 100, 4, 8;
404, 17244, 15324, 3148, 628, 116, 16;
528, 54252, 54476, 11672, 2152, 332, 44, 12;
972, 151992, 158468, 37244, 7940, 1120, 224, 48, 12, 16;
1404, 379488, 404148, 103436, 20216, 3316, 600, 132, 20, 16;
1896, 868460, 923656, 252096, 49848, 7916, 1744, 276, 84;
.
.

Cf. A360351 (vertices), A360352 (regions), A360353 (edges), A360354 (k-gons), A360350 (distinct circles), A359935.

Sum of row n = A360352(n).

A359932 Number of vertices among all distinct circles that can be constructed from an n x n square grid of points using only a compass.

Original entry on oeis.org

40, 689, 7240, 38729, 151584, 488741

Offset: 2

Scott R. Shannon, Jan 19 2023

A circle is constructed for every pair of the n x n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed from the n x n points is A359931(n).

No formula for a(n) is known.

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

Cf. A359933 (regions), A359934 (edges), A359935 (k-gons), A359931 (distinct circles), A359859, A359252.

a(n) = A359934(n) - A359933(n) + 1 by Euler's formula.

A359933 Number of regions among all distinct circles that can be constructed from an n X n square grid of points using only a compass.

Original entry on oeis.org

45, 836, 8197, 43252, 167157, 535572

Offset: 2

Scott R. Shannon, Jan 21 2023

A circle is constructed for every pair of the n X n points; the first point defines the circle's center while the second defines the radius. The number of distinct circles constructed from the n X n points is A359931(n).

No formula for a(n) is known.

Scott R. Shannon, Image for n = 2. In this and other images the n X n grid points are shown as white dots.
Scott R. Shannon, Image for n = 3.
Scott R. Shannon, Image for n = 4.
Scott R. Shannon, Image for n = 5.

Cf. A359932 (vertices), A359934 (edges), A359935 (k-gons), A359931 (distinct circles), A359860, A359253.

a(n) = A359934(n) - A359932(n) + 1 by Euler's formula.

A361623 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 using only a compass.

Original entry on oeis.org

0, 40, 60, 12, 0, 484, 583, 160, 28, 8, 0, 2196, 2416, 804, 104, 28, 0, 5676, 6616, 2184, 460, 40, 8, 13456, 16936, 5236, 1340, 104, 12, 4, 27512, 35032, 11796, 2400, 320, 28, 0, 4, 0, 50688, 65044, 22536, 4632, 584, 60, 12, 4, 8, 84300, 105860, 38024, 8124, 1080, 108

Offset: 1

Scott R. Shannon, Mar 18 2023

A circle is constructed for every pair of the 1 + 4n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed from the points is A361622(n).

See A354605 and A353782 for images of the vertices and regions.

			The table begins:
 0, 40, 60, 12;
 0, 484, 583, 160, 28, 8;
 0, 2196, 2416, 804, 104, 28;
 0, 5676, 6616, 2184, 460, 40;
 8, 13456, 16936, 5236, 1340, 104, 12;
 4, 27512, 35032, 11796, 2400, 320, 28, 0, 4;
 0, 50688, 65044, 22536, 4632, 584, 60, 12, 4;
 8, 84300, 105860, 38024, 8124, 1080, 108;
.
.

Cf. A354605 (vertices), A353782 (regions), A356358 (edges), A361622 (distinct circles), A359935, A359862, A359258, A359619, A359061.

Sum of row n = A353782(n).

A359934 Number of edges among all distinct circles that can be constructed from an n x n square grid of points using only a compass.

Original entry on oeis.org

84, 1524, 15436, 81980, 318740, 1024312

Offset: 2

Scott R. Shannon, Jan 21 2023

A circle is constructed for every pair of the n x n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed from the n x n points is A359931(n).
No formula for a(n) is known.
See A359932 and A359933 for images of the circles.

Cf. A359932 (vertices), A359933 (regions), A359935 (k-gons), A359931 (distinct circles), A359861, A359254.

a(n) = A359932(n) + A359933(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

A359931 Number of distinct circles that can be constructed from an n x n square grid of points using only a compass.

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A360354 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 an n x n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle.

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A359932 Number of vertices among all distinct circles that can be constructed from an n x n square grid of points using only a compass.

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A359933 Number of regions among all distinct circles that can be constructed from an n X n square grid of points using only a compass.

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A361623 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 using only a compass.

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A359934 Number of edges among all distinct circles that can be constructed from an n x n square grid of points using only a compass.

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