A008987 Number of immersions of an unoriented circle into the oriented sphere with n double points.

1, 1, 2, 6, 21, 99, 588, 3829, 27404, 206543, 1626638, 13242275, 110865868, 950078474, 8307074080, 73908443799, 667684486429

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• more

References

• V. I. Arnold, Topological Invariants of Plane Curves and Caustics, American Math. Soc., 1994, p. 18.

Links

• 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.
• Guy Valette, A Classification of Spherical Curves Based on Gauss Diagrams, Arnold Math J. (2016) 2:383-405.

Crossrefs

Cf. A008986, A008988, A008989. First line of triangle A260848.

Programs

Magma

// see A260848

Extensions

a(6)-a(7) from Guy Valette, Feb 09 2004

a(8)-a(9) from Robert Coquereaux and Jean-Bernard Zuber, Jul 21 2015

a(10) from same source added by N. J. A. Sloane, Mar 03 2016

a(11)-a(14) from Brendan McKay, Mar 11 2023

a(15)-a(16) from Brendan McKay, Mar 29 2024