A359968 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 equal the Farey series of order n.

3, 6, 37, 195, 1467, 3408, 17113, 40435, 109638, 191718, 572939, 842487, 2139708, 3231583, 5261013

Offset

1,1

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) - A359969(n) + 1 by Euler's formula.

Crossrefs

Cf. A359969 (regions), A359970 (edges), A359971 (k-gons), A005728, A360042, A359974, A359690, A358949, A358887.

Sequence in context: A093800 A068776 A355544 * A025596 A172361 A114038

Adjacent sequences: A359965 A359966 A359967 * A359969 A359970 A359971

Keyword

nonn,more

Author

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

Status

approved