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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.
10
5, 13, 69, 289, 1971, 3997, 20371, 45751, 120957, 205299, 629847, 897801, 2334409, 3461459, 5517131, 8468061
(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) - 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: A156101 A372799 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

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Last modified November 7 19:25 EST 2024. Contains 377536 sequences.
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