A008983 Number of immersions of the unoriented circle into the unoriented plane with n double points.

1, 2, 5, 20, 82, 435, 2645, 18489, 141326, 1153052, 9819315, 86305315, 776868505

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• more

References

• V. I. Arnold, Topological Invariants of Plane Curves and Caustics, American Math. Soc., 1994, p. 16.

Links

• S. R. Finch, Knots, links and tangles
• S. R. Finch, Knots, links and tangles, Aug 08 2003. [Cached copy, with permission of the author]
• S. M. Gusein-Zade and F. S. Duzhin, On the number of topological types of plane curves (Russian), Uspekhi Mat. Nauk 53 (1998), no. 3(321), 197-198. English translation: Russian Mathematical Surveys 53 (1998) 626-627. Related program and data.
• Christoph Lamm, The enumeration of doubly symmetric diagrams for strongly positive amphicheiral knots, arXiv:2410.06601 [math.GT], 2024. See p. 14.

Crossrefs

Cf. A008980, A008981, A008982, A008984, A008985, A054993.

Cf. A008989 (immersions into sphere), A118814 (tree-like immersions).

Extensions

Additional comments from Sergei Duzhin, Nov 11 2000

a(11)-a(12) from Sean A. Irvine, Apr 19 2018