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

1, 2, 5, 18, 70, 323, 1683, 9690, 59917, 388894, 2606742, 17869870, 124516636, 878591340

Offset: 0

Author

Moshe Shmuel Newman, May 23 2006

Keywords

• nonn
• more

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.

Examples

			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.
		

References

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

Links

• Andrei Zabolotskii, closed_curves - a program computing the sequence (2025).

Crossrefs

Cf. A008983.

Extensions

a(5)-a(11) from Andrei Zabolotskii, Jan 16 2025

a(12)-a(13) from Andrei Zabolotskii, Aug 15 2025