A359976 Number of edges formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions on one edge equal the Farey series of order n while on the other they divide its length into n equal segments.

3, 10, 55, 202, 902, 1868, 5886, 11676, 24322, 39440, 84155, 120151, 228121, 324856, 474396, 670552, 1104433, 1402237, 2185044, 2761367, 3654893, 4628608, 6706612, 8005739, 10770733

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Jan 20 2023

Keywords

• nonn
• more

Comments

The number of vertices on the edge with point positions equaling the Farey series of order n is A005728(n). No formula for a(n) is known.

See A359974 and A359975 for images of the triangle.

This graph is related to the 'Farey fan' given in the reference.

References

• McIlroy, M. D. "A Note on Discrete Representation of Lines". AT&T Technical Journal, 64 (1985), 481-490.

Crossrefs

Cf. A359974 (vertices), A359975 (regions), A359977 (k-gons), A005728, A359970, A359693, A358950, A358888.

Formula

a(n) = A359974(n) + A359975(n) - 1 by Euler's formula.