A359969 Number of regions formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions equal the Farey series of order n.

1, 5, 48, 239, 1798, 3950, 19953, 46007, 123338, 213793, 637960, 930635, 2361080, 3542822, 5736344

Offset: 1

Author

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

Keywords

• nonn
• more

Comments

The number of vertices along the shorter edges is A005728(n). No formula for a(n) is known. The sequence is inspired by the Farey fan; see A360042.

Links

• 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.

Crossrefs

Cf. A359968 (vertices), A359970 (edges), A359971 (k-gons), A005728, A360042, A359975, A359690, A358948, A358886.

Formula

a(n) = A359970(n) - A359968(n) + 1 by Euler's formula.