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.

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

Offset

1,2

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.

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) - 2*A005728(n).

Crossrefs

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

Sequence in context: A142511 A236070 A059705 * A218201 A015568 A322667

Adjacent sequences: A359688 A359689 A359690 * A359692 A359693 A359694

Keyword

nonn,more,changed

Author

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

Status

approved