A359974 Number of vertices 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, 6, 26, 93, 424, 876, 2785, 5542, 11575, 18761, 40249, 57399, 109376, 155965, 227884, 322377, 532454, 676282, 1056010, 1334975, 1767798, 2240664, 3252047, 3882192, 5226897

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.

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.

Scott R. Shannon, Image for n = 2.

Scott R. Shannon, Image for n = 3.

Scott R. Shannon, Image for n = 4.

Scott R. Shannon, Image for n = 5.

Scott R. Shannon, Image for n = 6.

Formula

a(n) = A359976(n) - A359975(n) + 1 by Euler's formula.

Crossrefs

Cf. A359975 (regions), A359976 (edges), A359977 (k-gons), A005728, A359968, A359690, A358949, A358887.

Sequence in context: A058258 A376970 A215397 * A214309 A005646 A033194

Adjacent sequences: A359971 A359972 A359973 * A359975 A359976 A359977

Keyword

nonn,more

Author

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

Status

approved