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).

3, 21, 375, 2574, 22083, 52791, 279750, 673050, 1851816, 3272058, 9865560, 14592537

Offset

1,1

Comments

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

See A358948 and A358949 for images of the square.

Links

Table of n, a(n) for n=1..12.

Wikipedia, Farey sequence.

Formula

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

Crossrefs

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

Sequence in context: A101389 A353321 A108716 * A271570 A084620 A120603

Adjacent sequences: A358947 A358948 A358949 * A358951 A358952 A358953

Keyword

nonn,more

Author

Scott R. Shannon and N. J. A. Sloane, Dec 07 2022

Status

approved