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.

A372977 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, using only a compass.

Original entry on oeis.org

40, 553, 4204, 14505, 39004, 94365, 197464, 320925, 569600
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.

Crossrefs

Cf. A372978 (regions), A372979 (edges), A372980 (k-gons), A372981 (circles), A372614, A372731, A371373, A354605, A360351.

Formula

a(n) = A372979(n) - A372978(n) + 1 by Euler's formula.

A372981 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, using only a compass.

Original entry on oeis.org

8, 32, 88, 160, 264, 400, 576, 732, 968, 1184, 1480, 1728, 2104, 2424, 2840, 3196, 3688, 4088, 4640, 5048, 5704, 6248, 6904, 7364
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 A372978 for images of the circles.

Crossrefs

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.

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.

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

Views

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.

A372980 Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, 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

16, 29, 272, 260, 80, 12, 4, 1708, 2253, 528, 120, 20, 4, 5200, 7636, 2136, 432, 44, 20, 8, 13732, 20788, 5712, 1120, 184, 17, 8, 31576, 49284, 14060, 3180, 584, 108, 16, 64748, 103557, 30372, 6472, 980, 172, 4, 12, 103368, 166804, 49920, 11196, 1660, 260, 48, 16, 181376, 296388, 88916, 19844, 3128, 445, 64, 20
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.
Unlike A372617, a similar sequence but with vertices on an equilateral triangle, for the terms studied no graph has 2-edged regions.
See A372977 and A372978 for images of the circles.

Examples

			The table begins:
16, 29;
272, 260, 80, 12, 4;
1708, 2253, 528, 120, 20, 4;
5200, 7636, 2136, 432, 44, 20, 8;
13732, 20788, 5712, 1120, 184, 17, 8;
31576, 49284, 14060, 3180, 584, 108, 16;
64748, 103557, 30372, 6472, 980, 172, 4, 12;
103368, 166804, 49920, 11196, 1660, 260, 48, 16;
181376, 296388, 88916, 19844, 3128, 445, 64, 20;
.
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Crossrefs

Cf. A372977 (vertices), A372978 (regions), A372979 (edges), A372981 (circles), A372617, A371376, A361623, A360354.

Formula

Sum of row n = A372978(n).
Showing 1-6 of 6 results.