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 A378831 #19 Dec 18 2024 09:21:44 %S A378831 1,2,2,4,5,10,11,21 %N A378831 The minimum number of diagonal lines required to cover all vertices created when the n outer vertices of a regular n-gon are connected by diagonal lines. %C A378831 See A007569 for the total number of vertices created by the diagonal lines of a regular n-gon. %C A378831 The terms a(9)..a(13) are less than or equal to 21, 25, 38, 41, 59 respectively. %C A378831 Note that these numbers are not always the same as the minimum number of required lines if the lines can be arbitrarily placed. The first known occurrence where the numbers differ is for a(7) = 10 where one can use eight diagonal lines plus one off-diagonal line to cover two vertices in such a way that all vertices can be covered with only 9 lines. %C A378831 Better upper bounds for a(10)..a(13) are 23, 36, 38, 56, with a(10), a(11) being almost certainly the correct values. - _Scott R. Shannon_, Dec 10 2024 %H A378831 Scott R. Shannon, <a href="/A378831/a378831.png">Image showing one example of 11 diagonals covering all 57 vertices of the octagon</a>. The covering diagonals are shown as thicker white lines. %Y A378831 Cf. A007569, A373813, A373811. %K A378831 nonn,more %O A378831 2,2 %A A378831 _Scott R. Shannon_, Dec 08 2024 %E A378831 a(9) added by _Scott R. Shannon_, Dec 10 2024