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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.
3
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
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Feb 23 2024
STATUS
approved