cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

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.

Original entry on oeis.org

13, 46, 99, 164, 257, 370, 503, 648, 821, 1014, 1227, 1444, 1697, 1970, 2255
Offset: 1

Views

Author

Scott R. Shannon, Mar 18 2023

Keywords

Comments

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.

Crossrefs

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

Views

Author

Scott R. Shannon, Mar 13 2023

Keywords

Comments

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.

Crossrefs

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

Formula

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

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

Views

Author

Scott R. Shannon, Mar 13 2023

Keywords

Comments

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.

Crossrefs

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

Formula

a(n) = A356358 - A353782(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

Views

Author

Scott R. Shannon, Mar 18 2023

Keywords

Comments

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.

Examples

			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;
.
.
		

Crossrefs

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

Formula

Sum of row n = A353782(n).

A372616 Number of curved edges 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

12, 207, 1104, 4359, 14880, 32523, 73662, 121605, 223290, 329286, 554286, 722841, 1145091
Offset: 0

Views

Author

Scott R. Shannon, May 07 2024

Keywords

Comments

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.
See A372614 and A372615 for images of the circles.

Crossrefs

Cf. A372614 (vertices), A372615 (regions), A372617 (k-gons), A372682 (number of circles), A371375, A356358, A360353.

Formula

a(n) = A372614(n) + A372615(n) - 1 by Euler's formula.

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

Views

Author

Scott R. Shannon, May 19 2024

Keywords

Comments

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.
See A372977 and A372978 for images of the circles.

Crossrefs

Cf. A372977 (vertices), A372978 (regions), A372980 (k-gons), A372981 (circles), A372616, A371375, A356358, A360353.

Formula

a(n) = A372977(n) + A372978(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

Views

Author

Scott R. Shannon, Apr 13 2023

Keywords

Comments

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.

Crossrefs

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

Formula

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

A372733 Number of curved edges 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 when every pair of the 3 + 3*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

12, 138, 738, 2838, 7194, 17904, 33954, 62868, 103866, 167280, 248826, 370458, 511806, 715905, 952608, 1260366
Offset: 0

Views

Author

Scott R. Shannon, May 12 2024

Keywords

Comments

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.
See A372731 and A372732 for images of the circles.

Crossrefs

Cf. A372731 (vertices), A372732 (regions), A372734 (k-gons), A372735 (number of circles), A372616, A371375, A356358, A360353.

Formula

a(n) = A372731(n) + A372732(n) - 1 by Euler's formula.
Showing 1-8 of 8 results.