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 A385161 #12 Jul 24 2025 09:31:26 %S A385161 1,117,4713,41173,233365,725081,2323869 %N A385161 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join a circle through every unordered triple of non-collinear points: a(n) is the number of distinct (finite) regions created. %H A385161 Scott R. Shannon, <a href="/A385161/a385161.jpg">Image for n = 2</a>. The 4 x 2 = 8 starting points are shown as white dots. %H A385161 Scott R. Shannon, <a href="/A385161/a385161_1.jpg">Image for n = 3</a>. The 4 x 3 = 12 starting points are shown as white dots. %F A385161 a(n) = A385162(n) - A385160(n) + 1 by Euler's formula. %Y A385161 Cf. A385159 (total circles), A385160 (vertices), A385162 (edges), A384702, A374826, A372977, A359570. %K A385161 nonn,more %O A385161 1,2 %A A385161 _Scott R. Shannon_, Jul 10 2025