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%I #14 Jan 30 2023 10:32:29
%S 3,6,37,195,1467,3408,17113,40435,109638,191718,572939,842487,2139708,
%T 3231583,5261013
%N Number of vertices formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions equal the Farey series of order n.
%C The number of vertices along the shorter edges is A005728(n). No formula for a(n) is known. The sequence is inspired by the Farey fan; see A360042.
%H Scott R. Shannon, <a href="/A359968/a359968.png">Image for n = 2</a>.
%H Scott R. Shannon, <a href="/A359968/a359968_1.png">Image for n = 3</a>.
%H Scott R. Shannon, <a href="/A359968/a359968_2.png">Image for n = 4</a>.
%H Scott R. Shannon, <a href="/A359968/a359968_3.png">Image for n = 5</a>.
%H Scott R. Shannon, <a href="/A359968/a359968_4.png">Image for n = 6</a>.
%F a(n) = A359970(n) - A359969(n) + 1 by Euler's formula.
%Y Cf. A359969 (regions), A359970 (edges), A359971 (k-gons), A005728, A360042, A359974, A359690, A358949, A358887.
%K nonn,more
%O 1,1
%A _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 20 2023
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