A359653 Number of regions 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.

1, 4, 96, 728, 7840, 17744, 104136, 246108, 681704, 1187200, 3719496, 5396692, 14149896

Offset

1,2

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) - A359654(n) + 1 by Euler's formula.

Crossrefs

Cf. A359654 (vertices), A359655 (edges), A359656 (k-gons), A005728, A358886, A358882, A355798, A358948, A006842, A006843.

Sequence in context: A068114 A272109 A203316 * A202682 A089639 A269091

Adjacent sequences: A359650 A359651 A359652 * A359654 A359655 A359656

Keyword

nonn,more

Author

Scott R. Shannon and N. J. A. Sloane, Jan 09 2023

Status

approved