A359691 - OEIS

%I #8 Feb 16 2025 08:34:04

%S 1,7,59,275,1949,3971,20333,45705,120899,205233,629761,897707,2334291,

%T 3461329,5516985,8467899

%N Number of crossings in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n.

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

%C See A359690 for images of the graph.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteBipartiteGraph.html">Complete Bipartite Graph</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Farey_sequence">Farey sequence</a>.

%F a(n) = A359690(n) - 2*A005728(n).

%Y Cf. A359690 (vertices), A359692 (regions), A359693 (edges), A359694 (k-gons), A005728, A159065, A331755, A359654, A358887, A358883, A006842, A006843.

%K nonn,more,changed

%O 1,2

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 11 2023