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 1-4 of 4 results.

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

Views

Author

Scott R. Shannon, Apr 12 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.

Crossrefs

Cf. A362234 (regions), A362235 (edges), A362236 (k-gons), A139275 (distinct circles), A354605, A359932.

Formula

a(n) = A362235(n) - A362234(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

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.

Crossrefs

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

Formula

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

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.

A373109 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 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.

Original entry on oeis.org

8, 4, 40, 76, 20, 60, 492, 304, 56, 20, 88, 1696, 1136, 252, 64, 16, 124, 4196, 3536, 1052, 204, 28, 4, 128, 8940, 7948, 2448, 496, 68, 0, 4, 172, 16464, 17628, 5560, 1268, 164, 4, 144, 28424, 30884, 9964, 2064, 312, 24, 8, 0, 8, 196, 46844, 51840, 17832, 4112, 556, 60, 20
Offset: 0

Views

Author

Scott R. Shannon, May 25 2024

Keywords

Comments

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.
See A373106 and A373107 for images of the circles.

Examples

			The table begins:
8, 4;
40, 76, 20;
60, 492, 304, 56, 20;
88, 1696, 1136, 252, 64, 16;
124, 4196, 3536, 1052, 204, 28, 4;
128, 8940, 7948, 2448, 496, 68, 0, 4;
172, 16464, 17628, 5560, 1268, 164, 4;
144, 28424, 30884, 9964, 2064, 312, 24, 8, 0, 8;
196, 46844, 51840, 17832, 4112, 556, 60, 20;
216, 71944, 80760, 28468, 6272, 856, 136, 0, 4;
264, 106588, 126856, 45148, 10780, 1628, 172, 32, 20;
.
.
		

Crossrefs

Cf. A373106 (vertices), A373107 (regions), A373108 (edges), A373110 (circles), A372980, A372734, A359009, A362236, A360354.

Formula

Sum of row n = A373107(n).
Showing 1-4 of 4 results.