A008986 Number of immersions of oriented circle into oriented sphere with n double points.

1, 1, 3, 9, 37, 182, 1143, 7553, 54559, 412306, 3251240, 26478264, 221714164, 1900103364, 16613990484, 147816411921, 1335367515821

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• more

Comments

a(10) = 3251240 by sampling method (to be confirmed, cf. ref. arXiv:1507.03163). - Robert Coquereaux, Nov 23 2015

a(10) = 3251240 confirmed. - Brendan McKay, Mar 29 2024

References

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

Links

• R. Coquereaux and J.-B. Zuber, Maps, immersions and permutations, 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
• Guy Valette, A Classification of Spherical Curves Based on Gauss Diagrams, Arnold Math J. (2016) 2:383-405.

Crossrefs

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

Programs

Magma

/* For Magma program see A260285. */

Extensions

a(6)-a(7) from Guy Valette, Feb 09 2004

a(8)-a(9) from Robert Coquereaux and Jean-Bernard Zuber, Jul 21 2015

a(10) from same source added by N. J. A. Sloane, Mar 03 2016

a(11)-a(16) from Brendan McKay, Mar 29 2024