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 1-6 of 6 results.

A373106 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 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

5, 61, 677, 2533, 7705, 17269, 37161, 65089, 111877, 174545, 274213
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.

Crossrefs

Cf. A373107 (regions), A373108 (edges), A373109 (k-gons), A373110 (circles), A372977, A372731, A358746, A362233, A360351.

Formula

a(n) = A373108(n) - A373107(n) + 1 by Euler's formula.

A373110 Number of 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

5, 22, 54, 99, 159, 232, 320, 421, 537, 666, 810, 967, 1139, 1324, 1524, 1737, 1965, 2206, 2462, 2731, 3015, 3312, 3624, 3949
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.

Crossrefs

Formula

Conjectured:
For even n, a(n) = (14*n^2 + 21*n + 10)/2.
For odd n, a(n) = (14*n^2 + 21*n + 9)/2.

A384703 On a 2 X n grid of vertices, draw a circle through every unordered triple of non-collinear vertices: a(n) is the number of distinct edges in the planar graph formed from the intersections of the circles.

Original entry on oeis.org

0, 4, 54, 416, 2182, 7884, 23294, 56982, 126310, 253564, 477462, 844524, 1424316
Offset: 1

Views

Author

Keywords

Comments

The edges being counted are of course arcs of circles.

Crossrefs

Cf. A384700 (circles), A384701 (vertices), A384702 (regions), A359571, A374827, A374339, A373108.

Formula

a(n) = A384701(n) + A384702(n) - 1 by Euler's formula, for n > 1.

A373107 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 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

12, 136, 932, 3252, 9144, 20032, 41260, 71832, 121460, 188656, 291488
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.

Crossrefs

Cf. A373106 (vertices), A373108 (edges), A373109 (k-gons), A373110 (circles), A372978, A372732, A358782, A362234, A360352.

Formula

a(n) = A373108(n) - A373106(n) + 1 by Euler's formula.

A385162 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join a circle through every unordered triple of non-collinear points: a(n) is the number of distinct (curved) edges formed from the intersections of the circles.

Original entry on oeis.org

4, 184, 8956, 79272, 455664, 1420624, 4576632
Offset: 1

Views

Author

Scott R. Shannon, Jul 10 2025

Keywords

Crossrefs

Cf. A385159 (total circles), A385160 (vertices), A385161 (regions), A384703, A374827, A373108, A359571.

Formula

a(n) = A385160(n) + A385161(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;
.
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Crossrefs

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

Formula

Sum of row n = A373107(n).
Showing 1-6 of 6 results.