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 A309318 #39 Jun 11 2025 17:21:26 %S A309318 1,2,24,180,2700,74184,2062800,81067840,3912595776 %N A309318 a(n) is the number of polygons whose vertices are the (2*n+1)-th roots of unity and whose 2*n+1 sides all have distinct slopes. %C A309318 The polygons are counted as nonequivalent by reflection and rotation. %C A309318 No even-sided polygons follow this rule. %C A309318 This is the number of harmonious labelings on a cycle. See A329910 for the definition of harmonious labelings. - _Wenjie Fang_, Oct 14 2022 %H A309318 Giovanni Resta, <a href="/A309318/a309318.pdf">Illustration of a(3) and a(4)</a> %H A309318 Ludovic Schwob, <a href="https://arxiv.org/abs/2506.04007">On the enumeration of double cosets and self-inverse double cosets</a>, arXiv:2506.04007 [math.CO], 2025. See p. 9. %e A309318 For n=2, the a(2)=2 solutions for 2*2+1 = 5 sides are the regular pentagon and pentagram. %Y A309318 Cf. A001710 (number of polygons with n-1 sides), A329910. %K A309318 nonn,more %O A309318 1,2 %A A309318 _Ludovic Schwob_, Jul 23 2019 %E A309318 a(7)-a(9) from _Giovanni Resta_, Jul 27 2019