A231346 Number of distinct polygonal shapes after n-th stage in the structure of the D-toothpick cellular automaton of A220500.

0, 0, 0, 1, 3, 4, 5, 7, 8, 8, 8, 11, 15, 17, 18, 19, 19, 19, 19, 19, 22

Offset: 1

Author

Omar E. Pol, Dec 07 2013

Keywords

• nonn
• hard
• more

Comments

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?

Links

• Omar E. Pol, Illustration of the structure of A220500 after 17 stages, (Contains 19 distinct polygonal shapes.)
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to toothpick sequences

Crossrefs

Cf. A139250, A194276, A220500, A220512, A220514, A220520, A220522, A220524, A220526.