login
Number of irreducible indecomposable spherical curves with n crossings (only ordinary double points), the circle is oriented, the sphere is oriented (OO case).
5

%I #25 Mar 30 2024 12:15:17

%S 0,0,1,1,2,6,17,73,290,1274,5844,27750,135192,676263,3437509,17811771,

%T 93531354,497835030,2680058068,14577839412,80039070868,443164758244,

%U 2472713506356

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

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

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

%H J. Betrema, <a href="https://github.com/j2b2/TaitCurves">Tait Curves</a>

%H R. Coquereaux and J.-B. Zuber, <a href="http://arxiv.org/abs/1507.03163">Maps, immersions and permutations</a>, arXiv preprint arXiv:1507.03163 [math.CO], 2015-2016. Also J. Knot Theory Ramifications 25, 1650047 (2016), DOI: <a href="https://doi.org/10.1142/S0218216516500474">10.1142/S0218216516500474</a>.

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

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

%K nonn,more

%O 1,5

%A _Robert Coquereaux_, Nov 23 2015

%E a(15)-a(16) using J. Betrema's program added by _Andrey Zabolotskiy_, Aug 24 2023

%E a(17)-a(23) from _Brendan McKay_, Mar 30 2024