A008981 Number of immersions of the unoriented circle into the oriented plane with n double points.

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

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

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

Cf. A008980, A008982, A008983, A008984, A008985, A054993.

Cf. A172023. - Parthasarathy Nambi, Jan 22 2010

Sequence in context: A174080 A337283 A115087 * A008982 A185134 A347497

Adjacent sequences: A008978 A008979 A008980 * A008982 A008983 A008984

Keyword

nonn,nice,hard,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