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 A386559 #10 Aug 02 2025 10:02:44 %S A386559 5,65,381,1213,3033,6105,12285,20789,33705,51065,79797,110817,161549, %T A386559 216985,284269,367925,489953,609225,785045,952877,1157749,1404473 %N A386559 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the number of points where lines intersect in the resulting graph. %C A386559 It appears that for n >= 3 the intersection that is furthest from the origin is formed by the crossing of the lines y = n/(n-1)*x + n and y = (n-1)/(n-2)*x - (n-1), along with the seven other symmetrically equivalent intersections. These intersections have a distance from the origin of approximately sqrt(8)*n^3 as n -> infinity. %H A386559 Scott R. Shannon, <a href="/A386559/a386559.png">Image for n = 1</a>. %H A386559 Scott R. Shannon, <a href="/A386559/a386559_1.png">Image for n = 2</a>. %H A386559 Scott R. Shannon, <a href="/A386559/a386559_2.png">Image for n = 3</a>. %H A386559 Scott R. Shannon, <a href="/A386559/a386559_3.png">Image for n = 4</a>. %F A386559 a(n) = A386561(n) - A386560(n) + 1 by Euler's formula. %Y A386559 Cf. A386560 (regions), A386561 (edges), A386562 (k-gons), A146212, A347750, A344657, A345649. %K A386559 nonn,more %O A386559 1,1 %A A386559 _Scott R. Shannon_, Jul 26 2025