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A008981 Number of immersions of the unoriented circle into the oriented plane with n double points. 6


%S 1,2,5,21,102,639,4492,34032,272252,2267905,19502386,172111844,

%T 1551948268

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

%C See Table 1, column 3 of E. D. Demaine et al. paper. - _Parthasarathy Nambi_, Jan 22 2010

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

%H 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 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 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.

%o (Pascal) Cf. link.

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

%Y Cf. A172023. - _Parthasarathy Nambi_, Jan 22 2010

%K nonn,nice,hard,more

%O 0,2

%A _N. J. A. Sloane_

%E Additional comments from _Sergei Duzhin_, Nov 11 2000

%E a(11)-a(12) from _Sean A. Irvine_, Apr 19 2018

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Last modified July 12 13:27 EDT 2020. Contains 335663 sequences. (Running on oeis4.)