A353782 -id:A353782 - 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)

A354605 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 using only a compass.

Original entry on oeis.org

101, 1145, 5001, 13753, 34497, 72185, 135157, 224321

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.

Cf. A353782 (regions), A356358 (edges), A361623 (k-gons), A361622 (distinct circles), A359932, A359859, A359252, A359569, A331702.

a(n) = A356358 - A353782(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).

A372615 Number of regions 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

7, 121, 624, 2368, 7912, 17115, 38461, 63184, 115614, 170149, 285715, 371982, 588043

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.

The vertices of the initial equilateral triangle are indicated by small circles in the illustrations here.

Scott R. Shannon, Image for n = 0.
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. A372614 (vertices), A372616 (edges), A372617 (k-gons), A372682 (number of circles), A371374, A353782, A360352.

a(n) = A372616(n) - A372614(n) + 1 by Euler's formula.

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

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 as white dots for clarity.
Scott R. Shannon, Image for n = 1.
Scott R. Shannon, Image for n = 2.
Scott R. Shannon, Image for n = 3.

Cf. A372977 (vertices), A372979 (edges), A372980 (k-gons), A372981 (circles), A372615, A371374, A353782, A360352.

a(n) = A372979(n) - A372977(n) + 1 by Euler's formula.

A372732 Number of regions 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

7, 88, 438, 1567, 3910, 9504, 17905, 32833, 54066, 86365, 128380, 190152, 262699, 365761, 486711, 642154

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.
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. A372731 (vertices), A372733 (edges), A372734 (k-gons), A372735 (number of circles), A372615, A371374, A353782, A360352.

a(n) = A372733(n) - A372731(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.

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.

Views

Author

Keywords

Comments

Crossrefs

A354605 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 using only a compass.

Views

Author

Keywords

Comments

Links

Crossrefs

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.

Views

Author

Keywords

Comments

Crossrefs

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.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

A372615 Number of regions 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.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

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.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

Views

Author

Keywords

Comments

Links

Crossrefs

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.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula