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.

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A371255 Number of (curved) edges formed when n equally spaced points are placed around a circle and all pairs of points are joined by an interior arc whose radius equals the circle's radius.

Original entry on oeis.org

1, 2, 9, 8, 40, 24, 168, 152, 477, 490, 1199, 912, 2418, 2464, 4230, 4464, 7769, 6894, 12369, 12400, 18606, 19008, 27784, 26376, 39575, 39390, 54027, 54432, 73254, 68340, 96410, 96800, 124443, 125222, 159005, 156168, 200540, 201932, 248508, 250120
Offset: 1

Views

Author

Scott R. Shannon, Mar 16 2024

Keywords

Comments

See A371253 and A371254 for images of the circles.

Crossrefs

Cf. A371253 (regions), A371254 (vertices), A371274 (k-gons), A135565, A358783, A359047, A359254.

Formula

a(n) = A371253(n) + A371254(n) - 1 by Euler's formula.

A370977 Let G_n denote the planar graph defined in A358746 with the addition, if n is odd, of the circle containing the initial n points; sequence gives the number of edges in G_n.

Original entry on oeis.org

1, 2, 15, 16, 125, 138, 539, 432, 1557, 1450, 3707, 3120, 7501, 6874, 13575, 12000, 23273, 20970, 36347, 32400, 54873, 51194, 79695, 70752, 113125, 105274, 154791, 144480, 206741, 195810, 272831, 255808, 352209, 335002, 446775, 422784, 560957, 534698, 695799, 659440, 850381, 815682
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Mar 25 2024

Keywords

Comments

If n is even the circle through the initial n points is already part of the graph.
In other words, draw a circle and place n equally spaced points around it; for each pair of poins X, Y, draw a circle with diameter XY; the union of these circles is the graph G_n.
For the numbers of vertices and regions in G_n see A358746 and A370976.
For other images for n even, see A358746 (for even n, A358783 and the present sequence agree).

Links

Crossrefs

Cf. A358746, A358782, A358783, A370976, A370978, A370979.

Formula

a(n) = A358783(n) if n even, a(n) = A358783(n) + n if n odd.

A370978 Draw a regular n-gon and the enclosing circle, then for each pair of vertices X, Y, draw a circle with diameter XY; the union of these figures is the graph H_n; sequence gives number of regions in H_n.

Original entry on oeis.org

1, 3, 16, 16, 81, 91, 302, 272, 829, 831, 1926, 1752, 3849, 3739, 6916, 6464, 11799, 11143, 18374, 17180, 27679, 26819, 40136, 37200, 56901, 54679, 77788, 74816, 103821, 101071, 136928, 131776, 176683, 172143, 224036, 216936, 281201, 273867, 348700, 337520, 426073, 416683
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Mar 25 2024

Keywords

Comments

H_n is the union of the graph G_n defined in A370976 and the polygon through the initial n points.

Links

Crossrefs

Cf. A358746, A358782, A358783, A370976, A370977, A370979.

Formula

a(n) = A358782(n) + n if n even, a(n) = A358782(n) + 3*n if n odd.
Previous Showing 11-13 of 13 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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