A359654 Number of vertices formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square.

4, 9, 77, 593, 6749, 15569, 93281, 222933, 623409, 1087393, 3453289, 5011009, 13271517

Offset

1,1

Comments

The number of points internal to each edge is given by A005728(n) - 2.

Links

Table of n, a(n) for n=1..13.

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) = A359655(n) - A359653(n) + 1 by Euler's formula.

Crossrefs

Cf. A359653 (regions), A359655 (edges), A359656 (k-gons), A005728, A358887, A358883, A355799, A358949, A006842, A006843.

Sequence in context: A041597 A041030 A361067 * A061104 A082381 A155931

Adjacent sequences: A359651 A359652 A359653 * A359655 A359656 A359657

Keyword

nonn,more

Author

Scott R. Shannon and N. J. A. Sloane, Jan 10 2023

Status

approved