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.

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

Offset: 1

Author

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

Keywords

• nonn
• more

Comments

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

Links

• 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.

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.