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.

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

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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.

A384702 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 (finite) regions created.

Original entry on oeis.org

0, 1, 37, 245, 1205, 4213, 12261, 29742, 65507, 130824, 245325, 432262, 727259
Offset: 1

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Author

Keywords

Comments

The infinite exterior region is not counted.

Crossrefs

Cf. A384700 (circles), A384701 (vertices), A384703 (edges), A359570, A374826, A374337, A372978.

Formula

a(n) = A384703(n) - A384701(n) + 1 by Euler's formula, for n > 1.

A384701 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 points where circles intersect.

Original entry on oeis.org

2, 4, 18, 172, 978, 3672, 11034, 27241, 60804, 122741, 232138, 412263, 697058
Offset: 1

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Author

Keywords

Crossrefs

Cf. A384700 (circles), A384702 (regions), A384703 (edges), A359569, A374825, A374338, A373106.

Formula

a(n) = A384703(n) - A384702(n) + 1 by Euler's formula, for n > 1.

A385159 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 circles created.

Original entry on oeis.org

1, 18, 99, 280, 633, 1098, 1915, 2928, 4329, 6010, 8331, 10752, 14113, 17778, 21987
Offset: 1

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Author

Scott R. Shannon, Jun 20 2025

Keywords

Crossrefs

Cf. A385160 (vertices), A385161 (regions), A385162 (edges), A361622, A384700, A373110, A372735, A365669.
Showing 1-4 of 4 results.