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A008983
Number of immersions of the unoriented circle into the unoriented plane with n double points.
7
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
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. A008989 (immersions into sphere), A118814 (tree-like immersions).
Sequence in context: A186767 A009737 A280624 * A286284 A286285 A192101
KEYWORD
nonn,nice,more
EXTENSIONS
Additional comments from Sergei Duzhin, Nov 11 2000
a(11)-a(12) from Sean A. Irvine, Apr 19 2018
STATUS
approved