|
%I #14 Dec 06 2022 19:33:37
%S 5,37,705,4549,42357,94525,531485,1250681,3440621,5985201
%N Number of vertices 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).
%C The number of points along each edge is given by A005728(n).
%H Scott R. Shannon, <a href="/A358887/a358887.png">Image for n = 1</a>.
%H Scott R. Shannon, <a href="/A358887/a358887_1.png">Image for n = 2</a>.
%H Scott R. Shannon, <a href="/A358887/a358887_2.png">Image for n = 3</a>.
%H Scott R. Shannon, <a href="/A358887/a358887_3.png">Image for n = 4</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Farey_sequence">Farey sequence</a>.
%F a(n) = A358888(n) - A358886(n) + 1 by Euler's formula.
%Y Cf. A358888 (edges), A358886 (regions), A358889 (k-gons), A006842, A006843, A005728, A358882, A358883.
%Y 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.
%K nonn,more
%O 1,1
%A _Scott R. Shannon_ and _N. J. A. Sloane_, Dec 05 2022
| 