cp's OEIS Frontend

A359976 Number of edges 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.

%I A359976 #14 Jan 30 2023 10:33:52
%S A359976 3,10,55,202,902,1868,5886,11676,24322,39440,84155,120151,228121,
%T A359976 324856,474396,670552,1104433,1402237,2185044,2761367,3654893,4628608,
%U A359976 6706612,8005739,10770733
%N A359976 Number of edges 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 A359976 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 A359976 See A359974 and A359975 for images of the triangle.
%C A359976 This graph is related to the 'Farey fan' given in the reference.
%D A359976 McIlroy, M. D. "A Note on Discrete Representation of Lines". AT&T Technical Journal, 64 (1985), 481-490.
%F A359976 a(n) = A359974(n) + A359975(n) - 1 by Euler's formula.
%Y A359976 Cf. A359974 (vertices), A359975 (regions), A359977 (k-gons), A005728, A359970, A359693, A358950, A358888.
%K A359976 nonn,more
%O A359976 1,1
%A A359976 _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 20 2023