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A370068 Number of nonequivalent directed unicursal star polygons (no edge joins adjacent vertices) that can be formed by connecting the vertices of a regular n-gon up to rotations.

%I A370068 #7 Mar 01 2024 15:28:57
%S A370068 0,0,0,0,2,1,10,47,350,3005,28722,302519,3471738,43181993,578730766,
%T A370068 8317664191,127644961618,2083638325661,36055062511490,659316772258655,
%U A370068 12705552903848466,257373902883624297,5467702595346969530,121562217391867941767
%N A370068 Number of nonequivalent directed unicursal star polygons (no edge joins adjacent vertices) that can be formed by connecting the vertices of a regular n-gon up to rotations.
%C A370068 Directed means that the direction of travel is significant.
%H A370068 Andrew Howroyd, <a href="/A370068/b370068.txt">Table of n, a(n) for n = 1..200</a>
%H A370068 Wikipedia, <a href="https://en.wikipedia.org/wiki/Unicursal_hexagram">Unicursal hexagram</a>.
%o A370068 (PARI)
%o A370068 Q(n,k)={subst(serlaplace(polcoef((1 - 2*x - x^2)/((1 + x)*(1 + (1 - y)*x + y*x^2)) + O(x^n), n-1)), y, k)}
%o A370068 E(r,d)={eulerphi(d)*Q(r,d) + 2*(-1)^r}
%o A370068 a370068(n)={if(n<3, 0, sumdiv(n,d,eulerphi(d)*E(n/d,d))/n)}
%Y A370068 Cf. A002619 (if edges may join adjacent vertices), A231091 (undirected), A326411, A370459.
%K A370068 nonn
%O A370068 1,5
%A A370068 _Andrew Howroyd_, Feb 23 2024