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.

A359653 Number of regions formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square.

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%I A359653 #8 Jan 10 2023 18:21:25
%S A359653 1,4,96,728,7840,17744,104136,246108,681704,1187200,3719496,5396692,
%T A359653 14149896
%N A359653 Number of regions formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square.
%C A359653 The number of points internal to each edge is given by A005728(n) - 2.
%H A359653 Scott R. Shannon, <a href="/A359653/a359653.jpg">Image for n = 2</a>.
%H A359653 Scott R. Shannon, <a href="/A359653/a359653_1.jpg">Image for n = 3</a>.
%H A359653 Scott R. Shannon, <a href="/A359653/a359653_2.jpg">Image for n = 4</a>.
%H A359653 Scott R. Shannon, <a href="/A359653/a359653_3.jpg">Image for n = 5</a>.
%H A359653 Scott R. Shannon, <a href="/A359653/a359653_4.jpg">Image for n = 6</a>.
%F A359653 a(n) = A359655(n) - A359654(n) + 1 by Euler's formula.
%Y A359653 Cf. A359654 (vertices), A359655 (edges), A359656 (k-gons), A005728, A358886, A358882, A355798, A358948, A006842, A006843.
%K A359653 nonn,more
%O A359653 1,2
%A A359653 _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 09 2023