|
%I #12 Nov 08 2017 12:11:23
%S 0,0,0,1,3,4,5,7,8,8,8,11,15,17,18,19,19,19,19,19,22
%N Number of distinct polygonal shapes after n-th stage in the structure of the D-toothpick cellular automaton of A220500.
%C The cellular automaton of A220500 contains a large number of distinct polygonal shapes. The exact number is unknown. Apparently it's greater than 63.
%C For simplicity we also call polygonal shapes "polygons".
%C In order to construct this sequence we use the following rules:
%C - Consider only the convex polygons and the concave polygons. Self-intersecting polygons are not counted.
%C - Unfinished polygons with inward growth are not counted.
%C - If two polygons have the same shape but they have different size then these polygons must be counted as distinct polygonal shapes.
%C - The reflected shapes of asymmetric polygons, both with the same area, must be counted as distinct polygonal shapes.
%C Question: Is there a maximal record in this sequence?
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poltp070.jpg">Illustration of the structure of A220500 after 17 stages</a>, (Contains 19 distinct polygonal shapes.)
%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%H <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%Y Cf. A139250, A194276, A220500, A220512, A220514, A220520, A220522, A220524, A220526.
%K nonn,hard,more
%O 1,5
%A _Omar E. Pol_, Dec 07 2013
| 