A118814 Number of 'tree-like curves' with n intersection points.

1, 2, 5, 18, 70, 323, 1683, 9690, 59917, 388894, 2606742, 17869870

Offset

0,2

Comments

The objects being enumerated are a subset of those enumerated by A008983. The restriction involved is that the Gauss diagram (or chord diagram) has no intersecting chords.

References

V. I. Arnold, Topological Invariants of plane curves and caustics, AMS, 1994, page 12.

Links

Table of n, a(n) for n=0..11.

Andrey Zabolotskiy, closed_curves - a program computing the sequence (2025).

Example

The first 3 entries are the same as A008983 because, for less than 3 intersection points, all curves are tree-like. For 3 intersection points there are only 2 curves that are not tree-like. They appear as the 4th and 15th entries in the table for n=3, on page 14 of Arnold's book.

Crossrefs

Cf. A008983.

Sequence in context: A073157 A365120 A268570 * A141494 A189843 A045612

Adjacent sequences: A118811 A118812 A118813 * A118815 A118816 A118817

Keyword

nonn,more

Author

Moshe Shmuel Newman, May 23 2006

Extensions

a(5)-a(11) from Andrey Zabolotskiy, Jan 16 2025

Status

approved