A264760 Number of irreducible indecomposable spherical curves with n crossings (only ordinary double points), the circle is not oriented, the sphere is oriented (UO case).

0, 0, 1, 1, 2, 4, 12, 41, 161, 658, 2993, 13974, 67945, 338644, 1720544, 8908579, 46775073, 248932094, 1340079951, 7289000415, 40019815872, 221582832331, 123635832467

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 disjoint 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: http://dx.doi.org/10.1142/S0218216516500474
• Gunnar Brinkmann and Brendan McKay, plantri plane graph generator. To obtain this sequence use options -Guoqc2m2d (which makes plane quartic graphs) and count those for which the straight-ahead Eulerian walk has a single component.

Crossrefs

Cf. A008986, A008987, A008988, A008989, A007756, A264759, A264761.

Programs

C

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

Extensions

a(14)-a(21) from Brendan McKay, Mar 12 2023

plantri link added by Brendan McKay, Mar 25 2024

a(22) and a(23) from Brendan McKay, Mar 30 2024