A118814 - OEIS

%I #12 Apr 25 2024 14:34:31

%S 1,2,5,18,70

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

%C 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.)

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

%Y Cf. A008983.

%K nonn

%O 0,2

%A _Moshe Shmuel Newman_, May 23 2006