A354605 -id:A354605 - cp's OEIS frontend

A361622 Number of 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.

13, 46, 99, 164, 257, 370, 503, 648, 821, 1014, 1227, 1444, 1697, 1970, 2255

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.
No formula for a(n) is known.
See A354605 and A353782 for images of the resulting vertices and regions.

Cf. A354605 (vertices), A353782 (regions), A356358 (edges), A361623 (k-gons)

A353782 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 using only a compass.

Original entry on oeis.org

112, 1264, 5548, 14976, 37092, 77096, 143560, 237504

Offset: 1

Scott R. Shannon, Mar 13 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).

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. A354605 (vertices), A356358 (edges), A361623 (k-gons), A361622 (distinct circles), A359933, A359860, A359253, A359570, A359046.

a(n) = A356358 - A354605(n) + 1 by Euler's formula.

A356358 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 using only a compass.

Original entry on oeis.org

212, 2408, 10548, 28728, 71588, 149280, 278716, 461824

Offset: 1

Scott R. Shannon, Mar 13 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).
No formula for a(n) is known.
See A354605 and A353782 for images of the vertices and regions.

Cf. A354605 (vertices), A353782 (regions), A361623 (k-gons), A361622 (distinct circles), A359934, A359861, A359254, A359571, A359047.

a(n) = A353782(n) + A354605(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).

A372614 Number of vertices among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle, using only a compass.

Original entry on oeis.org

6, 87, 481, 1992, 6969, 15409, 35202, 58422, 107677, 159138, 268572, 350860, 557049

Offset: 0

Scott R. Shannon, May 07 2024

A circle is constructed for every pair of the 3 + 3*n points, the first point defines the circle's center while the second the radius distance.

Scott R. Shannon, Image for n = 0. In this and other images the 3 + 3*n vertices forming the triangle 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.
Scott R. Shannon, Image for n = 4.

Cf. A372615 (regions), A372616 (edges), A372617 (k-gons), A372682 (number of circles), A372731, A371373, A354605, A360351.

a(n) = A372616(n) - A372615(n) + 1 by Euler's formula.

A372731 Number of vertices among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3n points placed on the sides of an equilateral triangle when every pair of the 3 + 3n points are connected by a circle and where the points lie at the ends of the circle's diameter.

Original entry on oeis.org

6, 51, 301, 1272, 3285, 8401, 16050, 30036, 49801, 80916, 120447, 180307, 249108, 350145, 465898, 618213

Offset: 0

Scott R. Shannon, May 12 2024

A circle is constructed for every pair of the 3 + 3*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 3 + 3*n vertices forming the triangle 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.
Scott R. Shannon, Image for n = 4.

Cf. A372732 (regions), A372733 (edges), A372734 (k-gons), A372735 (number of circles), A372614, A371373, A354605, A360351.

a(n) = A372733(n) - A372732(n) + 1 by Euler's formula.

A372977 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, using only a compass.

Original entry on oeis.org

40, 553, 4204, 14505, 39004, 94365, 197464, 320925, 569600

Offset: 0

Scott R. Shannon, May 19 2024

A circle is constructed for every pair of the 4 + 4*n points, the first point defines the circle's center while the second the radius distance.

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. A372978 (regions), A372979 (edges), A372980 (k-gons), A372981 (circles), A372614, A372731, A371373, A354605, A360351.

a(n) = A372979(n) - A372978(n) + 1 by Euler's formula.

A362233 Number of vertices 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

17, 249, 1381, 4745, 12581, 26861, 51649, 89357, 145501, 225621, 335497

Offset: 1

Scott R. Shannon, Apr 12 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. A362234 (regions), A362235 (edges), A362236 (k-gons), A139275 (distinct circles), A354605, A359932.

a(n) = A362235(n) - A362234(n) + 1 by Euler's formula.

cp's OEIS Frontend

A361622 Number of 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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A353782 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 using only a compass.

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A356358 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 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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A372614 Number of vertices among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle, using only a compass.

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A372977 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, using only a compass.

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A362233 Number of vertices 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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