A212413 Anchored partitions of a circle

1, 1, 2, 9, 63

Offset

0,3

Comments

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.

Links

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

Jon Wild, Illustration for a(3)=9 and a(4)=63

Example

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.

Crossrefs

Sequence in context: A100262 A166886 A377843 * A003577 A085928 A130169

Adjacent sequences: A212410 A212411 A212412 * A212414 A212415 A212416

Keyword

nonn

Author

Jon Wild, May 15 2012

Status

approved