cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A359974 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 on one edge equal the Farey series of order n while on the other they divide its length into n equal segments.

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%I A359974 #13 Jan 30 2023 10:33:36
%S A359974 3,6,26,93,424,876,2785,5542,11575,18761,40249,57399,109376,155965,
%T A359974 227884,322377,532454,676282,1056010,1334975,1767798,2240664,3252047,
%U A359974 3882192,5226897
%N A359974 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 on one edge equal the Farey series of order n while on the other they divide its length into n equal segments.
%C A359974 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 A359974 This graph is related to the 'Farey fan' given in the reference.
%D A359974 McIlroy, M. D. "A Note on Discrete Representation of Lines". AT&T Technical Journal, 64 (1985), 481-490.
%H A359974 Scott R. Shannon, <a href="/A359974/a359974.png">Image for n = 2</a>.
%H A359974 Scott R. Shannon, <a href="/A359974/a359974_1.png">Image for n = 3</a>.
%H A359974 Scott R. Shannon, <a href="/A359974/a359974_2.png">Image for n = 4</a>.
%H A359974 Scott R. Shannon, <a href="/A359974/a359974_3.png">Image for n = 5</a>.
%H A359974 Scott R. Shannon, <a href="/A359974/a359974_4.png">Image for n = 6</a>.
%F A359974 a(n) = A359976(n) - A359975(n) + 1 by Euler's formula.
%Y A359974 Cf. A359975 (regions), A359976 (edges), A359977 (k-gons), A005728, A359968, A359690, A358949, A358887.
%K A359974 nonn,more
%O A359974 1,1
%A A359974 _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 20 2023