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A008981
Number of immersions of the unoriented circle into the oriented plane with n double points.
6
1, 2, 5, 21, 102, 639, 4492, 34032, 272252, 2267905, 19502386, 172111844, 1551948268
OFFSET
0,2
COMMENTS
See Table 1, column 3 of E. D. Demaine et al. paper. - Parthasarathy Nambi, Jan 22 2010
REFERENCES
V. I. Arnold, Topological Invariants of Plane Curves and Caustics, American Math. Soc., 1994, p. 16.
LINKS
E. D. Demaine, M. L. Demaine, P. Taslakian and G. T. Toussaint, Sand drawings and Gaussian graphs, Journal of Mathematics and the Arts, 1 (2007), 125-133.
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.
S. M. Gusein-Zade and F. S. Duzhin, Enumeration of plane curves with up to 10 selfintersections, Pascal program and result table, 05 Apr 1998.
Christoph Lamm, The enumeration of doubly symmetric diagrams for strongly positive amphicheiral knots, arXiv:2410.06601 [math.GT], 2024. See p. 14.
PROG
(Pascal) Cf. link.
CROSSREFS
KEYWORD
nonn,nice,hard,more
EXTENSIONS
Additional comments from Sergei Duzhin, Nov 11 2000
a(11)-a(12) from Sean A. Irvine, Apr 19 2018
STATUS
approved