A359654 - OEIS

%I #8 Jan 10 2023 18:22:29

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

%T 13271517

%N 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.

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

%H Scott R. Shannon, <a href="/A359654/a359654.png">Image for n = 2</a>.

%H Scott R. Shannon, <a href="/A359654/a359654_1.png">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A359654/a359654_2.png">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A359654/a359654_3.png">Image for n = 5</a>.

%H Scott R. Shannon, <a href="/A359654/a359654_4.png">Image for n = 6</a>.

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

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

%K nonn,more

%O 1,1

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 10 2023