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

1,5

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.

Prog

(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)}

Crossrefs

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

Sequence in context: A304359 A054781 A213421 * A239070 A271042 A098290

Adjacent sequences: A370065 A370066 A370067 * A370069 A370070 A370071

Keyword

nonn

Author

Andrew Howroyd, Feb 23 2024

Status

approved