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 A370459 #23 Mar 06 2024 21:48:18
%S A370459 0,0,1,1,5,19,112,828,7441,76579,871225,10809051,144730446,2079635889,
%T A370459 31912025537,520913578812,9013780062785,164829273635749,
%U A370459 3176388519597555,64343477504391475,1366925655386979893,30390554390984325019,705740995420852895453
%N A370459 Number of unicursal stars with n vertices.
%C A370459 A unicursal star is a closed loop formed by diagonals of a regular n-gon.
%C A370459 These are Hamiltonian cycles on the graph complement of the n-cycle.
%C A370459 Allowing polygon diagonals, but not sides, is equivalent to requiring every edge to cross at least one other edge.
%C A370459 These are counted up to rotation and reflection, i.e., modulo dihedral symmetry of the n-gon.
%C A370459 Inspired by a unicursal dodecagram drawn by Gordon FitzGerald (see links).
%H A370459 Andrew Howroyd, <a href="/A370459/b370459.txt">Table of n, a(n) for n = 3..200</a>
%H A370459 Gordon FitzGerald, <a href="https://www.facebook.com/groups/391950357895182?multi_permalinks=1777073729382831">illustration of a unicursal dodecagram</a>.
%H A370459 Wikipedia, <a href="https://en.wikipedia.org/wiki/Unicursal_hexagram">Unicursal hexagram</a>.
%F A370459 a(n) = (A231091(n) + A370769(n))/2. - _Andrew Howroyd_, Mar 06 2024
%e A370459 For n=5, there is only the regular pentagram {5/2}.
%e A370459 For n=6, there is only the unicursal hexagram.
%e A370459 For n=7, in addition to the two regular heptagrams {7/2} and {7/3}, there are three nontrivial unicursal heptagrams represented by:
%e A370459 (0, 2, 4, 1, 6, 3, 5, 0)
%e A370459 (0, 2, 5, 1, 3, 6, 4, 0)
%e A370459 (0, 2, 5, 1, 4, 6, 3, 0).
%o A370459 (PARI) \\ Requires a370068 from A370068.
%o A370459 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 A370459 Re(n)=subst(serlaplace(polcoef((1 - x - 2*x^2)/(4*(1 + (1 - 2*y)*x + 2*y*x^2)) + O(x*x^n), n)), y, 1)
%o A370459 a(n)={if(n<3, 0, (if(n%2, 2*Ro(n\2), Re(n/2)) + a370068(n))/4)} \\ _Andrew Howroyd_, Mar 01 2024
%Y A370459 Cf. A000940 (polygon sides allowed).
%Y A370459 Cf. A055684 (cases with dihedral symmetry only).
%Y A370459 Cf. A002816 (rotations and reflections counted separately).
%Y A370459 Cf. A231091 (up to rotations only), A370769 (achiral).
%K A370459 nonn
%O A370459 3,5
%A A370459 _Adam M. Scherlis_, Feb 19 2024
%E A370459 a(14) onwards from _Andrew Howroyd_, Feb 26 2024