A359655 Number of edges 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, 12, 172, 1320, 14588, 33312, 197416, 469040, 1305112, 2274592, 7172784, 10407700, 27421412

Offset

1,1

Comments

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

See A359653 and A359654 for images of the square.

Links

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

Formula

a(n) = A359653(n) + A359654(n) - 1 by Euler's formula.

Crossrefs

Cf. A359653 (regions) A359654 (vertices), A359656 (k-gons), A005728, A358888, A358884, A355800, A358950, A006842, A006843.

Sequence in context: A365310 A222393 A367883 * A213143 A173603 A175718

Adjacent sequences: A359652 A359653 A359654 * A359656 A359657 A359658

Keyword

nonn,more

Author

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

Status

approved