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

1,5

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

Table of n, a(n) for n=1..21.

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.

Sequence in context: A247140 A269304 A071054 * A033545 A253570 A362580

Adjacent sequences: A231343 A231344 A231345 * A231347 A231348 A231349

Keyword

nonn,hard,more

Author

Omar E. Pol, Dec 07 2013

Status

approved