A007756 Number of irreducible indecomposable spherical curves with n crossings (only ordinary double points), the circle is oriented, the sphere is not oriented (OU case).

0, 0, 1, 1, 2, 3, 11, 38, 156, 638, 2973, 13882, 67868, 338147, 1720303, 8905996, 46774728, 248918004, 1340083514, 7288922610, 40019870539, 221582395052, 1236358849827

Offset

1,5

Comments

Old name was "Prime Gaussian (i.e. only ordinary double points) curves with n crossings."

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

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

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

C. Ernst, C. Hart, T. Menezes and D. Price, A complete list of minimal diagrams of an oriented alternating knot, J. Knot Theory Ramifications 30, 2150063 (2021). See section 3.1.

Prog

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

Crossrefs

Cf. A008986, A008987, A008988, A008989, A264759, A264760, A264761.

Sequence in context: A088747 A231574 A365288 * A000280 A249402 A046224

Adjacent sequences: A007753 A007754 A007755 * A007757 A007758 A007759

Keyword

nonn,more

Author

Jean Betrema

Extensions

Edited by Robert Coquereaux, Nov 23 2015

a(15)-a(16) from Sean A. Irvine, Jan 22 2018

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

Status

approved