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.

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

Offset

1,1

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.

Links

Table of n, a(n) for n=1..16.

Eric Weisstein's World of Mathematics, Complete Bipartite Graph.

Wikipedia, Farey sequence.

Formula

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

Crossrefs

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

Sequence in context: A122829 A232688 A221980 * A225827 A349498 A200904

Adjacent sequences: A359690 A359691 A359692 * A359694 A359695 A359696

Keyword

nonn,more

Author

Scott R. Shannon and N. J. A. Sloane, Jan 11 2023

Status

approved