|
%I #5 May 15 2012 12:39:20
%S 1,1,2,9,63
%N Anchored partitions of a circle
%C n line segments are drawn successively within a circle; they may not cross one another. When each segment is drawn, each of its endpoints must be "anchored"; that is, it must lie either on the circumference of the circle, or on a previously drawn segment. No two endpoints may coincide (thus no "V"s or "X"s). The sequence counts the topologically distinct partitions, and does not count separately partitions that are equivalent under mirror reflection.
%H Jon Wild, <a href="/A212413/a212413.pdf">Illustration for a(3)=9 and a(4)=63</a>
%e In the attached pdf file, the nine anchored partitions for n=3 are shown in the left-hand margin. For each, all partitions for n=4 are illustrated that can be derived from the n=3 cases by adding one line segment, except those that have already been derived from an earlier n=3 case.
%K nonn
%O 0,3
%A _Jon Wild_, May 15 2012
|
