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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

%I #6 Jan 10 2023 18:22:47

%S 4,12,172,1320,14588,33312,197416,469040,1305112,2274592,7172784,

%T 10407700,27421412

%N 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.

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

%C See A359653 and A359654 for images of the square.

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

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

%K nonn,more

%O 1,1

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