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

1,1

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

Crossrefs

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

Sequence in context: A149575 A156101 A093118 * A087506 A068487 A075063

Adjacent sequences: A359687 A359688 A359689 * A359691 A359692 A359693

Keyword

nonn,more

Author

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

Status

approved