A359692 Number of regions in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n.

2, 12, 94, 382, 2486, 4946, 24100, 53152, 138158, 233254, 700720, 999364, 2559344, 3785044, 6027148, 9210820

Offset

1,1

Comments

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

Links

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

Scott R. Shannon, Image for n = 1.

Scott R. Shannon, Image for n = 2.

Scott R. Shannon, Image for n = 3.

Scott R. Shannon, Image for n = 4.

Scott R. Shannon, Image for n = 5.

Scott R. Shannon, Image for n = 6.

Scott R. Shannon, Image for n = 7.

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

Wikipedia, Farey sequence.

Formula

a(n) = A359693(n) - A359690(n) + 1 by Euler's formula.

Crossrefs

Cf. A359690 (vertices), A359691 (crossings), A359693 (edges), A359694 (k-gons), A005728, A290131, A359653, A358886, A358882, A006842, A006843.

Sequence in context: A003123 A316143 A372202 * A321057 A366334 A247075

Adjacent sequences: A359689 A359690 A359691 * A359693 A359694 A359695

Keyword

nonn

Author

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

Status

approved