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

Links

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.

A374337 Start with two vertices and draw a circle around each whose radius is the distance between the vertices. The sequence gives the number of regions constructed after n iterations of drawing circles with this same radius around every new vertex created from all circles' intersections.

Original entry on oeis.org

3, 11, 27, 55, 99, 145, 203, 277, 353, 441, 545, 651, 769, 903, 1039, 1187, 1351, 1517, 1695, 1889, 2085, 2293, 2517, 2743, 2981, 3235, 3491, 3759, 4043, 4329, 4627, 4941, 5257, 5585, 5929, 6275, 6633, 7007, 7383, 7771, 8175, 8581, 8999, 9433, 9869, 10317, 10781, 11247, 11725, 12219, 12715
Offset: 1

Views

Author

Scott R. Shannon, Jul 05 2024

Keywords

Comments

See A374338 for further details.

Links

Crossrefs

Cf. A374338 (vertices), A374339 (edges), A359570, A371374, A371253.

Formula

a(n) = A374339(n) - A374338(n) + 1, by Euler's formula.
Conjectured:
If n = 3*k + 1, k >= 0, a(n) = |(15*n^2 - 17*n - 7)/3|.
If n = 3*k, k >= 1, a(n) = (15*n^2 - 17*n - 3)/3.
If n = 3*k - 1, k >= 1, a(n) = (15*n^2 - 17*n + 7)/3.

A384700 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 circles created.

Original entry on oeis.org

0, 1, 9, 24, 52, 93, 153, 232, 336, 465, 625, 816, 1044, 1309, 1617, 1968, 2368, 2817, 3321, 3880, 4500, 5181, 5929
Offset: 1

Views

Author

Scott R. Shannon and N. J. A. Sloane, Jun 07 2025

Keywords

Links

Crossrefs

Cf. A384701 (vertices), A384702 (regions), A384703 (edges), A365669, A374338, A373110, A372981,

Formula

Conjecture:
for even n, a(n) = n^3/2 - n^2/4 - n,
for odd n > 1, a(n) = n^3/2 - n^2/4 - n + 3/4.

A374339 Start with two vertices and draw a circle around each whose radius is the distance between the vertices. The sequence gives the number of curved edges constructed after n iterations of drawing circles with this same radius around every new vertex created from all circles' intersections.

Original entry on oeis.org

6, 18, 40, 78, 132, 190, 264, 354, 448, 558, 684, 814, 960, 1122, 1288, 1470, 1668, 1870, 2088, 2322, 2560, 2814, 3084, 3358, 3648, 3954, 4264, 4590, 4932, 5278, 5640, 6018, 6400, 6798, 7212, 7630, 8064, 8514, 8968, 9438, 9924, 10414, 10920, 11442, 11968, 12510, 13068, 13630, 14208, 14802
Offset: 1

Views

Author

Scott R. Shannon, Jul 05 2024

Keywords

Comments

See A374338 for further details and images.

Crossrefs

Cf. A374337 (regions), A374338 (vertices), A359571, A371375, A371255.

Formula

a(n) = A374337(n) + A374338(n) - 1, by Euler's formula.

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

Views

Author

Scott R. Shannon and N. J. A. Sloane, Jun 07 2025

Keywords

Links

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.
Showing 1-5 of 5 results.

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

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