cp's OEIS Frontend

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

%I A008981 #33 Oct 14 2024 11:22:24
%S A008981 1,2,5,21,102,639,4492,34032,272252,2267905,19502386,172111844,
%T A008981 1551948268
%N A008981 Number of immersions of the unoriented circle into the oriented plane with n double points.
%C A008981 See Table 1, column 3 of E. D. Demaine et al. paper. - _Parthasarathy Nambi_, Jan 22 2010
%D A008981 V. I. Arnold, Topological Invariants of Plane Curves and Caustics, American Math. Soc., 1994, p. 16.
%H A008981 E. D. Demaine, M. L. Demaine, P. Taslakian and G. T. Toussaint, <a href="http://dx.doi.org/10.1080/17513470701413451">Sand drawings and Gaussian graphs</a>, Journal of Mathematics and the Arts, 1 (2007), 125-133.
%H A008981 S. M. Gusein-Zade and F. S. Duzhin, <a href="http://www.pdmi.ras.ru/~arnsem/">On the number of topological types of plane curves</a>; (Russian) Uspekhi Mat. Nauk 53 (1998), no. 3(321), 197-198. <a href="https://pdfs.semanticscholar.org/8e15/31bc512538a6e0dcd2f22d638d94c5682610.pdf">English translation</a>: Russian Mathematical Surveys 53 (1998) 626-627.
%H A008981 S. M. Gusein-Zade and F. S. Duzhin, Enumeration of plane curves with up to 10 selfintersections, <a href="http://www.pdmi.ras.ru/~arnsem/dataprog/">Pascal program and result table</a>, 05 Apr 1998.
%H A008981 Christoph Lamm, <a href="https://arxiv.org/abs/2410.06601">The enumeration of doubly symmetric diagrams for strongly positive amphicheiral knots</a>, arXiv:2410.06601 [math.GT], 2024. See p. 14.
%o A008981 (Pascal) Cf. link.
%Y A008981 Cf. A008980, A008982, A008983, A008984, A008985, A054993.
%Y A008981 Cf. A172023. - _Parthasarathy Nambi_, Jan 22 2010
%K A008981 nonn,nice,hard,more
%O A008981 0,2
%A A008981 _N. J. A. Sloane_
%E A008981 Additional comments from _Sergei Duzhin_, Nov 11 2000
%E A008981 a(11)-a(12) from _Sean A. Irvine_, Apr 19 2018