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.

A359117 Number of regions in the planar Farey Ring graph FR(n) defined in A359116, including the regions between the convex hull and the bounding circle.

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%I A359117 #14 May 06 2025 11:26:06
%S A359117 1,2,8,30,250,548,3180,7468,20684,36164,112406,163600,425144,636208,
%T A359117 1028934,1581766,3323182,4249976,8216442,10668790,15329216
%N A359117 Number of regions in the planar Farey Ring graph FR(n) defined in A359116, including the regions between the convex hull and the bounding circle.
%H A359117 Scott R. Shannon, <a href="/A359117/a359117.jpg">Image for n = 3</a>.
%H A359117 Scott R. Shannon, <a href="/A359117/a359117_1.jpg">Image for n = 4</a>.
%H A359117 Scott R. Shannon, <a href="/A359117/a359117_2.jpg">Image for n = 5</a>.
%H A359117 Scott R. Shannon, <a href="/A359117/a359117_3.jpg">Image for n = 6</a>.
%H A359117 Scott R. Shannon, <a href="/A359117/a359117_4.jpg">Image for n = 7</a>.
%H A359117 Scott R. Shannon, <a href="/A359117/a359117_5.jpg">Image for n = 8</a>.
%H A359117 Scott R. Shannon, <a href="/A359117/a359117_6.jpg">Image for n = 9</a>.
%H A359117 Scott R. Shannon, <a href="/A359117/a359117_7.jpg">Image for n = 10</a>.
%F A359117 a(n) = A359118 - A359116 + 1 by Euler's formula.
%Y A359117 Cf. A359116 (vertices), A359118 (edges), A359119 (k-gons), A358886, A006842, A006843, A005728, A007678.
%K A359117 nonn,more
%O A359117 1,2
%A A359117 _Scott R. Shannon_ and _N. J. A. Sloane_, Dec 17 2022