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

1,2

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

Table of n, a(n) for n=1..15.

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

Crossrefs

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

Sequence in context: A247705 A215543 A212111 * A215050 A268785 A268736

Adjacent sequences: A359966 A359967 A359968 * A359970 A359971 A359972

Keyword

nonn,more

Author

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

Status

approved