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

1,5

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

Table of n, a(n) for n=1..23.

J. Betrema, Tait Curves

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.

Robert Coquereaux and Jean-Bernard Zuber, Maps, immersions and permutations, arXiv preprint arXiv:1507.03163 [math.CO], 2015-2016. Also J. Knot Theory Ramifications 25, 1650047 (2016), DOI: https://doi.org/10.1142/S0218216516500474

Prog

(C) // See the J. Betrema C program in the Tait Curves link.

Crossrefs

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

Sequence in context: A342225 A218144 A222919 * A090959 A244035 A340025

Adjacent sequences: A264757 A264758 A264759 * A264761 A264762 A264763

Keyword

nonn,more

Author

Robert Coquereaux, Nov 23 2015

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

Status

approved