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.

A359969 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 equal the Farey series of order n.

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%I A359969 #11 Jan 30 2023 10:32:40
%S A359969 1,5,48,239,1798,3950,19953,46007,123338,213793,637960,930635,2361080,
%T A359969 3542822,5736344
%N A359969 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 equal the Farey series of order n.
%C A359969 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 A359969 Scott R. Shannon, <a href="/A359969/a359969.jpg">Image for n = 2</a>.
%H A359969 Scott R. Shannon, <a href="/A359969/a359969_1.jpg">Image for n = 3</a>.
%H A359969 Scott R. Shannon, <a href="/A359969/a359969_2.jpg">Image for n = 4</a>.
%H A359969 Scott R. Shannon, <a href="/A359969/a359969_3.jpg">Image for n = 5</a>.
%H A359969 Scott R. Shannon, <a href="/A359969/a359969_4.jpg">Image for n = 6</a>.
%F A359969 a(n) = A359970(n) - A359968(n) + 1 by Euler's formula.
%Y A359969 Cf. A359968 (vertices), A359970 (edges), A359971 (k-gons), A005728, A360042, A359975, A359690, A358948, A358886.
%K A359969 nonn,more
%O A359969 1,2
%A A359969 _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 20 2023