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 A349784 #24 Dec 15 2022 05:12:47 %S A349784 3,3,4,5,4,6,5,6,4,8,5,7,6,8,7,8,8,7,8,8,6,8,8,8,8,11,6,10,7,8,8,9,8, %T A349784 10,8,8,12,10,8,14,10,9,8,10,10,10,10,12,8,12,10,10,10,10,10,12,9,12, %U A349784 10,12,10,12,9,10,10,10,10,11,10,12,10,12,12,10,10,10,10,10,10,10,10,12,10 %N A349784 Maximum number of sides in any cell in a regular n-gon with all diagonals drawn (cf. A007678), excluding the central n-sided cell for odd values of n. %C A349784 As a regular n-gon with an odd number of sides always creates an n-sided cell at its center when all its diagonals are drawn, see A342222, this n-sided cell is not considered for odd n. %C A349784 Although the behavior of the sequence is unknown as n -> infinity, the data up to n = 765 implies the sequence is possibly bounded. In the range studied the 14-gon is the predominant maximum-sided cell for n > 300. %C A349784 No n-gon is currently known that produces a cell with 17 sides or 19 sides and above, other than the corresponding central n-sided cell for odd values of n. %C A349784 See A342222 and A342236 for images of the n-gons. %H A349784 Scott R. Shannon, <a href="/A349784/b349784.txt">Table of n, a(n) for n = 4..765</a> %H A349784 Scott R. Shannon, <a href="/A349784/a349784.png">Image showing a close-up of the 18-sided cell in the 708-gon</a>. Zoom in to see the vertices marked as white dots around the 18-gon, shown in violet. The bottom three vertices are extremely close together -- if the image were expanded so that the outer two of these vertices were 1cm away from the inner vertex then the size of the entire 708-gon image would be slightly over 12.9 km in diameter. %e A349784 a(4) = 3 as a regular 4-gon (square) creates four 3-gons (triangles) when all its diagonals are drawn. %e A349784 a(5) = 3 as a regular 5-gon (pentagon) creates ten 3-gons when all its diagonals are drawn. Also created is a central 5-gon but this cell is not considered. %e A349784 a(6) = 4 as a regular 6-gon (hexagon) creates eighteen 3-gons and six 4-gons when all its diagonals are drawn. %e A349784 a(7) = 5 as a regular 7-gon (heptagon) creates thirty-five 3-gons, seven 4-gons and seven 5-gons when all its diagonals are drawn. Also created is a central 7-gon but this cell is not considered. %Y A349784 Cf. A341729, A342236, A007678, A331450. %K A349784 nonn %O A349784 4,1 %A A349784 _Scott R. Shannon_ and _N. J. A. Sloane_, Nov 30 2021