A358888 Number of edges formed inside a square with edge length 1 by the straight line segments mutually connecting all vertices and points that divide the sides into segments with lengths equal to the Farey series of order n = A006842(n,k)/A006843(n,k), k = 1..A005728(n).

8, 92, 1744, 10612, 95460, 210020, 1161404, 2708424, 7392884, 12820768

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Dec 05 2022

Keywords

• nonn
• more

Comments

The number of points along each edge is given by A005728(n).

See A358886 and A358887 for images of the square.

Links

• Wikipedia, Farey sequence.

Crossrefs

Cf. A358886 (regions), A358887 (vertices), A358889 (k-gons), A006842, A006843, A005728, A358882, A358884.

The Farey Diagrams Farey(m,n) are studied in A358298-A358307 and A358882-A358885, the Completed Farey Diagrams of order (m,n) in A358886-A358889.

Formula

a(n) = A358886(n) + A358887(n) - 1 by Euler's formula.