A358886 - OEIS

A358886

Number of regions 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).

4, 56, 1040, 6064, 53104, 115496, 629920, 1457744, 3952264, 6835568

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OFFSET

1,1

COMMENTS

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

We call this graph the Completed Farey Diagram of order (n,k). The (ordinary) Farey diagram Farey(n,k) is a subgraph. In the latter graph, not all pairs of boundary points are joined by lines.

LINKS

Table of n, a(n) for n=1..10.

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.

Wikipedia, Farey sequence.

FORMULA

a(n) = A358888(n) - A358887(n) + 1 by Euler's formula.

CROSSREFS