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

0,2

References

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

Links

Table of n, a(n) for n=0..12.

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).

Sequence in context: A186767 A009737 A280624 * A286284 A286285 A192101

Adjacent sequences: A008980 A008981 A008982 * A008984 A008985 A008986

Keyword

nonn,nice,more

Author

N. J. A. Sloane

Extensions

Additional comments from Sergei Duzhin, Nov 11 2000

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

Status

approved