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.

0, 0, 0, 0, 2, 1, 10, 47, 350, 3005, 28722, 302519, 3471738, 43181993, 578730766, 8317664191, 127644961618, 2083638325661, 36055062511490, 659316772258655, 12705552903848466, 257373902883624297, 5467702595346969530, 121562217391867941767

Offset: 1

Author

Andrew Howroyd, Feb 23 2024

Keywords

• nonn

Comments

Directed means that the direction of travel is significant.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Wikipedia, Unicursal hexagram.

Crossrefs

Cf. A002619 (if edges may join adjacent vertices), A231091 (undirected), A326411, A370459.

Programs

PARI

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)}
E(r,d)={eulerphi(d)*Q(r,d) + 2*(-1)^r}
a370068(n)={if(n<3, 0, sumdiv(n,d,eulerphi(d)*E(n/d,d))/n)}