A359655 Number of edges formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square.

4, 12, 172, 1320, 14588, 33312, 197416, 469040, 1305112, 2274592, 7172784, 10407700, 27421412

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Jan 10 2023

Keywords

• nonn
• more

Comments

The number of points internal to each edge is given by A005728(n) - 2.

See A359653 and A359654 for images of the square.

Crossrefs

Cf. A359653 (regions) A359654 (vertices), A359656 (k-gons), A005728, A358888, A358884, A355800, A358950, A006842, A006843.

Formula

a(n) = A359653(n) + A359654(n) - 1 by Euler's formula.