A008986 - OEIS

%I #57 Mar 30 2024 11:39:29

%S 1,1,3,9,37,182,1143,7553,54559,412306,3251240,26478264,221714164,

%T 1900103364,16613990484,147816411921,1335367515821

%N Number of immersions of oriented circle into oriented sphere with n double points.

%C a(10) = 3251240 by sampling method (to be confirmed, cf. ref. arXiv:1507.03163). - _Robert Coquereaux_, Nov 23 2015

%C a(10) = 3251240 confirmed. - _Brendan McKay_, Mar 29 2024

%D V. I. Arnold, Topological Invariants of Plane Curves and Caustics, American Math. Soc., 1994, p. 18.

%H R. Coquereaux and J.-B. Zuber, <a href="http://arxiv.org/abs/1507.03163">Maps, immersions and permutations</a>, arXiv preprint arXiv:1507.03163 [math.CO], 2015-2016. Also J. Knot Theory Ramifications 25, 1650047 (2016), DOI: http://dx.doi.org/10.1142/S0218216516500474

%H Guy Valette, <a href="https://doi.org/10.1007/s40598-016-0049-3">A Classification of Spherical Curves Based on Gauss Diagrams</a>, Arnold Math J. (2016) 2:383-405.

%o (Magma) /* For Magma program see A260285. */

%Y Cf. A008987, A008988, A008989. First line of triangle A260285.

%K nonn,more

%O 0,3

%A _N. J. A. Sloane_

%E a(6)-a(7) from _Guy Valette_, Feb 09 2004

%E a(8)-a(9) from _Robert Coquereaux_ and Jean-Bernard Zuber, Jul 21 2015

%E a(10) from same source added by _N. J. A. Sloane_, Mar 03 2016

%E a(11)-a(16) from _Brendan McKay_, Mar 29 2024