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

1,1

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.

Links

Table of n, a(n) for n=1..25.

Formula

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

Crossrefs

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

Sequence in context: A229311 A208480 A342966 * A034234 A284645 A081721

Adjacent sequences: A359973 A359974 A359975 * A359977 A359978 A359979

Keyword

nonn,more

Author

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

Status

approved