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.

A359690 Number of vertices in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n.

Original entry on oeis.org

5, 13, 69, 289, 1971, 3997, 20371, 45751, 120957, 205299, 629847, 897801, 2334409, 3461459, 5517131, 8468061
Offset: 1

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Author

Keywords

Comments

The number of vertices along each edge is A005728(n). No formula for a(n) is known.

Crossrefs

Cf. A359691 (crossings), A359692 (regions), A359693 (edges), A359694 (k-gons), A005728, A331755, A359654, A358887, A358883, A006842, A006843.

Formula

a(n) = A359693(n) - A359692(n) + 1 by Euler's formula.

A359694 Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n.

Original entry on oeis.org

2, 10, 2, 70, 24, 218, 160, 4, 1254, 1068, 148, 16, 2254, 2414, 252, 26, 10082, 11760, 1980, 266, 12, 21410, 25958, 5096, 648, 36, 4, 53422, 68208, 14360, 1980, 168, 20, 86986, 118922, 24028, 3056, 248, 12, 0, 2, 255678, 346676, 84344, 12774, 1132, 110, 4, 2, 365674, 493530, 119820, 18600, 1624, 112, 4
Offset: 1

Views

Author

Keywords

Comments

The number of vertices along each edge is A005728(n). No formula is known.
See A359692 for other images of the graph.

Examples

			The table begins:
2;
10, 2;
70, 24;
218, 160, 4;
1254, 1068, 148, 16;
2254, 2414, 252, 26;
10082, 11760, 1980, 266, 12;
21410, 25958, 5096, 648, 36, 4;
53422, 68208, 14360, 1980, 168, 20;
86986, 118922, 24028, 3056, 248, 12, 0, 2;
255678, 346676, 84344, 12774, 1132, 110, 4, 2;
365674, 493530, 119820, 18600, 1624, 112, 4;
917478, 1244492, 334096, 57080, 5700, 478, 16, 4;
1335398, 1862666, 495536, 82642, 8096, 676, 24, 6;
2107042, 2989864, 788340, 128378, 12536, 932, 52, 4;
3195474, 4557430, 1230300, 205352, 20516, 1664, 80, 4;
.
.
		

Crossrefs

Cf. A359690 (vertices), A359691 (crossings), A359692 (regions), A359693 (edges), A005728, A290131, A359653, A358886, A358882, A006842, A006843.

Formula

Sum of row n = A359692(n).

A359693 Number of edges in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n.

Original entry on oeis.org

6, 24, 162, 670, 4456, 8942, 44470, 98902, 259114, 438552, 1330566, 1897164, 4893752, 7246502, 11544278, 17678880
Offset: 1

Views

Author

Keywords

Comments

The number of vertices along each edge is A005728(n). No formula for a(n) is known.
See A359690 and A359692 for images of the graph.

Crossrefs

Cf. A359690 (vertices), A359691 (crossings), A359692 (regions), A359694 (k-gons), A005728, A290132, A359655, A358888, A358884, A006842, A006843.

Formula

a(n) = A359690(n) + A359692(n) - 2*A005728(n) + 1 by Euler's formula.

A359691 Number of crossings in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n.

Original entry on oeis.org

1, 7, 59, 275, 1949, 3971, 20333, 45705, 120899, 205233, 629761, 897707, 2334291, 3461329, 5516985, 8467899
Offset: 1

Views

Author

Keywords

Comments

The number of vertices along each edge is A005728(n). No formula for a(n) is known.
See A359690 for images of the graph.

Crossrefs

Cf. A359690 (vertices), A359692 (regions), A359693 (edges), A359694 (k-gons), A005728, A159065, A331755, A359654, A358887, A358883, A006842, A006843.

Formula

a(n) = A359690(n) - 2*A005728(n).
Showing 1-4 of 4 results.