%I #14 Jan 30 2023 10:33:44
%S 1,5,30,110,479,993,3102,6135,12748,20680,43907,62753,118746,168892,
%T 246513,348176,571980,725956,1129035,1426393,1887096,2387945,3454566,
%U 4123548,5543837
%N Number of regions formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions on one edge equal the Farey series of order n while on the other they divide its length into n equal segments.
%C The number of vertices on the edge with point positions equaling the Farey series of order n is A005728(n). No formula for a(n) is known.
%C This graph is related to the 'Farey fan' given in the reference.
%D McIlroy, M. D. "A Note on Discrete Representation of Lines". AT&T Technical Journal, 64 (1985), 481-490.
%H Scott R. Shannon, <a href="/A359975/a359975.jpg">Image for n = 2</a>.
%H Scott R. Shannon, <a href="/A359975/a359975_1.jpg">Image for n = 3</a>.
%H Scott R. Shannon, <a href="/A359975/a359975_2.jpg">Image for n = 4</a>.
%H Scott R. Shannon, <a href="/A359975/a359975_3.jpg">Image for n = 5</a>.
%H Scott R. Shannon, <a href="/A359975/a359975_4.jpg">Image for n = 6</a>.
%F a(n) = A359976(n) - A359974(n) + 1 by Euler's formula.
%Y Cf. A359974 (vertices), A359976 (edges), A359977 (k-gons), A005728, A359969, A359690, A358948, A358886.
%K nonn,more
%O 1,2
%A _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 20 2023