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 1-5 of 5 results.

A374825 Place n equally spaced points on the circumference of a circle of radius r and then connect each pair of points with straight lines whose intersections create A007569(n) - n additional points. Draw a circle of radius r around each of the A007569(n) points. The sequence gives the total number of vertices formed from all circle intersections.

Original entry on oeis.org

0, 1, 4, 13, 71, 313, 1625, 3073, 17443, 28601, 115094, 95965, 527463, 587441
Offset: 1

Views

Author

Scott R. Shannon, Jul 21 2024

Keywords

Crossrefs

Cf. A374826 (regions), A374827 (edges), A374828 (k-gons), A007569 (total circles), A370980, A374338.

Formula

a(n) = A374827(n) - A374826(n) + 1, by Euler's formula.

A374826 Place n equally spaced points on the circumference of a circle of radius r and then connect each pair of points with straight lines whose intersections create A007569(n) - n additional points. Draw a circle of radius r around each of the A007569(n) points. The sequence gives the total number of regions formed from all circle intersections.

Original entry on oeis.org

1, 2, 6, 16, 80, 324, 1666, 3120, 17703, 28780, 115401, 96624, 528073, 589708
Offset: 1

Views

Author

Scott R. Shannon, Jul 21 2024

Keywords

Crossrefs

Cf. A374825 (vertices), A374827 (edges), A374828 (k-gons), A007569 (total circles), A093005, A374337.

Formula

a(n) = A374827(n) - A374825(n) + 1, by Euler's formula.

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.

A374828 Irregular table read by rows: Place n equally spaced points on the circumference of a circle of radius r and then connect each pair of points with straight lines whose intersections create A007569(n) - n additional points. Draw a circle of radius r around each of the A007569(n) points. T(n,k) is the number of k-sided regions, k>=2, formed from all circle intersections.

Original entry on oeis.org

3, 3, 0, 12, 4, 5, 45, 10, 10, 10, 0, 156, 84, 48, 30, 6, 0, 742, 476, 294, 119, 21, 14, 0, 1104, 1296, 512, 152, 40, 16, 0, 6669, 6768, 2790, 1179, 207, 81, 9, 0, 10280, 11130, 5490, 1440, 260, 150, 20, 10, 0, 40777, 45342, 20669, 6963, 1177, 374, 77, 11, 11
Offset: 3

Views

Author

Scott R. Shannon, Jul 21 2024

Keywords

Comments

It is likely that n = 5 is the last graph that produces 2-sided regions, although this is unknown.

Examples

			The table begins:
3, 3;
0, 12, 4;
5, 45, 10, 10, 10;
0, 156, 84, 48, 30, 6;
0, 742, 476, 294, 119, 21, 14;
0, 1104, 1296, 512, 152, 40, 16;
0, 6669, 6768, 2790, 1179, 207, 81, 9;
0, 10280, 11130, 5490, 1440, 260, 150, 20, 10;
0, 40777, 45342, 20669, 6963, 1177, 374, 77, 11, 11;
0, 33672, 39552, 16236, 5772, 1080, 288, 0, 12, 0, 12;
0, 181467, 212186, 97461, 30082, 5252, 1430, 78, 104, 0, 0, 13;
0, 198772, 246134, 104356, 33348, 5614, 1190, 252, 28, 0, 0, 0, 14;
.
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Crossrefs

Cf. A374825 (vertices), A374826 (regions), A374827 (edges), A007569 (total circles).

Formula

Sum of row n = A374826(n).

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.
Showing 1-5 of 5 results.