A008987 Number of immersions of an unoriented circle into the oriented sphere with n double points.

1, 1, 2, 6, 21, 99, 588, 3829, 27404, 206543, 1626638, 13242275, 110865868, 950078474, 8307074080, 73908443799, 667684486429

Offset

0,3

References

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

Links

Table of n, a(n) for n=0..16.

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: 10.1142/S0218216516500474.

Guy Valette, A Classification of Spherical Curves Based on Gauss Diagrams, Arnold Math J. (2016) 2:383-405.

Prog

(Magma)  // see A260848

Crossrefs

Cf. A008986, A008988, A008989. First line of triangle A260848.

Sequence in context: A008988 A061232 A020091 * A079129 A305923 A130275

Adjacent sequences: A008984 A008985 A008986 * A008988 A008989 A008990

Keyword

nonn,more

Author

N. J. A. Sloane

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(14) from Brendan McKay, Mar 11 2023

a(15)-a(16) from Brendan McKay, Mar 29 2024

Status

approved