A359692 - OEIS

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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.

5

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

(list; graph; refs; listen; history; text; internal format)

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