A264761 Number of irreducible indecomposable spherical curves with n crossings (only ordinary double points), the circle is oriented, the sphere is oriented (OO case).

0, 0, 1, 1, 2, 6, 17, 73, 290, 1274, 5844, 27750, 135192, 676263, 3437509, 17811771, 93531354, 497835030, 2680058068, 14577839412, 80039070868, 443164758244, 2472713506356

Offset: 1

Author

Robert Coquereaux, Nov 23 2015

Keywords

• nonn
• more

Comments

Irreducible means not made disconnected by removal of a vertex (no nugatory crossings).

Indecomposable (or prime) means not made disconnected by cutting two distinct lines.

Links

• J. Betrema, Tait Curves
• R. Coquereaux and J.-B. Zuber, Maps, immersions and permutations, arXiv preprint arXiv:1507.03163 [math.CO], 2015-2016. Also J. Knot Theory Ramifications 25, 1650047 (2016), DOI: 10.1142/S0218216516500474.

Crossrefs

Cf. A008986, A008987, A008988, A008989, A007756, A264759, A264760.

Programs

C

See the J. Betrema C program in the Tait Curves link.

Extensions

a(15)-a(16) using J. Betrema's program added by Andrey Zabolotskiy, Aug 24 2023

a(17)-a(23) from Brendan McKay, Mar 30 2024