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.
%I A309889 #7 Aug 21 2019 15:00:35 %S A309889 1,1,2,10,36 %N A309889 a(n) is the maximal number of regions in the Euclidean plane made by superimposing a simple n-gon onto the resulting plane figure of a(n-1). %C A309889 There is initially one region and the 1-gon and 2-gon are ignored, so a(1) and a(2) result in one region. Each line of the n-gon should cross as many lines as possible and avoid intersecting previous intersections. %e A309889 For n = 3 the plane is empty, so the trigon can only create 1 extra region. Thus a(3) = 2. %e A309889 For n = 4 each tetragon edge intersects a maximum of 2 trigon edges, creating a total of 4 new regions. Two trigon edges intersect 2 tetragon edges, adding 4 regions, and the last trigon edge intersects all 4 tetragon edges, adding another 4 regions. Thus a(4) = 2 + 4 + 4 = 10. %Y A309889 Cf. A000124. %K A309889 nonn,more %O A309889 1,3 %A A309889 _Arran Ireland_, Aug 21 2019