A008989 Number of immersions of an unoriented circle into the unoriented sphere with n double points.

1, 1, 2, 6, 19, 76, 376, 2194, 14614, 106421, 823832, 6657811, 55557329, 475475046, 4155030702, 36959470662, 333860366236

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.

J. Cantarella, H. Chapman, and M. Mastin, Knot Probabilities in Random Diagrams, arXiv preprint arXiv:1512.05749 [math.GT], 2015. Also Journal of Physics A: Mathematical and Theoretical, Vol. 49, No. 40 (2016), DOI: 10.1088/1751-8113/49/40/405001

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), 10.1142/S0218216516500474.

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

Example

G.f. = 1 + x + 2*x^2 + 6*x^3 + 19*x^4 + 76*x^5 + 376*x^6 + 2194*x^7 + ...

Prog

(Magma)  // see A260914

Crossrefs

Cf. A008986, A008987, A008988, A264759, A277739. First line of triangle A260914.

Sequence in context: A268569 A181770 A138800 * A057240 A079564 A273988

Adjacent sequences: A008986 A008987 A008988 * A008990 A008991 A008992

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