A358950 - OEIS

A358950

Number of edges formed inside a triangle 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).

%I #6 Dec 19 2022 13:31:51

%S 3,21,375,2574,22083,52791,279750,673050,1851816,3272058,9865560,

%T 14592537

%N Number of edges formed inside a triangle 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).

%C See A358948 and A358949 for images of the square.

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

%F a(n) = A358948(n) + A358949(n) - 1 by Euler's formula.

%Y Cf. A358948 (regions), A358949 (vertices), A358951 (k-gons), A358888, A006842, A006843, A005728, A358882.

%K nonn,more

%O 1,1

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Dec 07 2022