cp's OEIS Frontend

All line segments are equal length. The initial pattern is a straight line segment. It has 2 free ends, so a(0)=2. The construction rules for generation n >= 1 are:

(i) subject to rule ii, add 2 line segments at each free end by arranging in a "V" shape with angle Pi/3 and connecting symmetrically to the free end (nearly like a 3-handed clock showing 07:00:25);

(ii) a "V" is not added if either of its segments would cross a line segment drawn in an earlier generation;

(iii) when generation n is complete, each new line segment clearly touches 2 line segments where it was initially attached; the other end of the new line segment counts as being free if the segment does not touch or cross any more line segments.

a(n) is the number of free ends created in generation n.

It seems that a(n) drops to 24 for n = 5, 9, 17, 33, 65, ... . See illustrations in the links.

The terms of this sequence should be checked! - Omar E. Pol, Apr 23 2015

The cellular automaton of A220500 contains a large number of distinct polygonal shapes. The exact number is unknown. Apparently it's greater than 63.

For simplicity we also call polygonal shapes "polygons".

In order to construct this sequence we use the following rules:

- Consider only the convex polygons and the concave polygons. Self-intersecting polygons are not counted.

- Unfinished polygons with inward growth are not counted.

- If two polygons have the same shape but they have different size then these polygons must be counted as distinct polygonal shapes.

- The reflected shapes of asymmetric polygons, both with the same area, must be counted as distinct polygonal shapes.

Question: Is there a maximal record in this sequence?