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 A370769 #6 Mar 06 2024 18:18:41 %S A370769 0,0,0,0,1,1,5,11,49,123,521,1583,6581,23239,95509,384771,1570265, %T A370769 7106995,28869825,145034327,587270877,3242792607,13100475021, %U A370769 78866628011,318067071169,2073381189259,8350998470777,58602568320255,235794888434053,1772311322357623 %N A370769 Number of achiral unicursal star polygons (no edge joins adjacent vertices) that can be formed by connecting the vertices of a regular n-gon. %C A370769 Achiral means that the polygon has an axis of reflective symmetry. %H A370769 Andrew Howroyd, <a href="/A370769/b370769.txt">Table of n, a(n) for n = 1..200</a> %F A370769 a(2*n+1) = A370766(n)/2 - A370768(n-1) for n >= 1. %F A370769 a(2*n) = (A370766(n-1)/2 - A370768(n-2) + A370766(n)/4 - A370768(n-1) + A283184(n-1)/2)/2 for n >= 2. %o A370769 (PARI) %o A370769 Ro(n)=-(-1)^n + subst(serlaplace(polcoef(((1 - x)^2)/(2*(1 + x)*(1 + (1 - 2*y)*x + 2*y*x^2)) + O(x*x^n), n)), y, 1) %o A370769 Re(n)=subst(serlaplace(polcoef((1 - 3*x)/(8*(1 + (1 - 2*y)*x + 2*y*x^2)) + O(x*x^n), n)), y, 1) %o A370769 a(n) = if(n < 3, 0, if(n % 2, Ro(n\2), Re(n/2))) %Y A370769 Cf. A283184, A370766, A370767, A370768. %Y A370769 Cf. A231091 (stars up to rotation), A370459 (up to rotation and reflection). %K A370769 nonn %O A370769 1,7 %A A370769 _Andrew Howroyd_, Mar 01 2024