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

1, 2, 5, 18, 70

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. 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. (For all I know, this sequence may be equal to one of the others already in the database with the same initial terms.)

References

V. I. Arnold's "Topological Invariants of plane curves and caustics", page 12.

Links

Table of n, a(n) for n=0..4.

Crossrefs

Cf. A008983.

Sequence in context: A288910 A249062 A322555 * A345878 A014271 A073157

Adjacent sequences: A118811 A118812 A118813 * A118815 A118816 A118817

Keyword

nonn

Author

Moshe Shmuel Newman, May 23 2006

Status

approved