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 A101364 #15 Jul 19 2024 13:27:38 %S A101364 0,0,0,0,0,1,0,0,0,12,0,0,0,0,0,54,0,0,0,0,0,264,0,0,0,0,0,420,0,0,0, %T A101364 0,0,396,0,0,0,0,0,1134,0,0,0,0,0,1200,0,0,0,0,0,1296,0,0,0,0,0,3780, %U A101364 0,0,0,0,0,2310,0,0,0,0,0,2520,0,0,0,0,0,3276,0,0,0,0,0,3612,0,0,0,0,0,4050 %N A101364 In the interior of a regular n-gon with all diagonals drawn, the number of points where exactly four diagonals intersect. %C A101364 When n is odd, there are no intersections in the interior of an n-gon where more than 2 diagonals meet. %C A101364 When n is not a multiple of 6, there are no intersections in the interior of an n-gon where more than 3 diagonals meet except the center. %C A101364 When n is not a multiple of 30, there are no intersections in the interior of an n-gon where more than 5 diagonals meet except the center. %C A101364 I checked the following conjecture up to n=210: "An n-gon with n=30k has 5n points where 6 or 7 diagonals meet and no interior point other than the center where more than 7 diagonals meet; If k is odd, then 6 diagonals meet in each of 4n points and 7 diagonals meet in each of n points; If k is even, then no groups of exactly 6 diagonals meet in a point, while exactly 7 diagonals meet in each of 5n points (all points interior excluding the center)." %H A101364 Seiichi Manyama, <a href="/A101364/b101364.txt">Table of n, a(n) for n = 3..10000</a> (terms 3..210 from Graeme McRae) %H A101364 <a href="/index/Pol#Poonen">Sequences formed by drawing all diagonals in regular polygon</a> %e A101364 a(18)=54 because inside a regular 18-gon there are 54 points where exactly four diagonals intersect. %Y A101364 A column of A292105. %Y A101364 Cf. A006561, A007678. %Y A101364 Cf. A000332: C(n, 4) = number of intersection points of diagonals of convex n-gon. %Y A101364 Cf. A006561: number of intersections of diagonals in the interior of regular n-gon. %Y A101364 Cf. A101363: number of 3-way intersections in the interior of a regular 2n-gon. %Y A101364 Cf. A101365: number of 5-way intersections in the interior of a regular n-gon. %Y A101364 Cf. A137938: number of 4-way intersections in the interior of a regular 6n-gon. %Y A101364 Cf. A137939: number of 5-way intersections in the interior of a regular 6n-gon. %K A101364 nonn %O A101364 3,10 %A A101364 _Graeme McRae_, Dec 26 2004, revised Feb 23 2008