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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
OFFSET
1,1
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved