

A194276


Number of distinct polygonal shapes after nth stage in the Dtoothpick structure of A194270.


6



0, 0, 0, 0, 1, 3, 4, 5, 6, 7, 9, 10, 10, 11, 13, 13, 14
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OFFSET

0,6


COMMENTS

The cellular automaton of A194270 contains a large number of distinct polygonal shapes. 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. Selfintersecting polygons are not counted. (Note that some polygons contain in their body a toothpick or Dtoothpick with an exposed endpoint; that element is not a part of the perimeter of the polygon.)
 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.
For more information see A194277 and A194278.
Question: Is there a maximal record in this sequence?


LINKS

Table of n, a(n) for n=0..16.
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to toothpick sequences


EXAMPLE

Consider toothpicks of length 2 and Dtoothpicks of length sqrt(2).
.
Stage New type Perimeter Area Term a(n)
. 0    a(0) = 0
. 1    a(1) = 0
. 2    a(2) = 0
. 3    a(3) = 0
. 4 hexagon 4*sqrt(2)+4 6 a(4) = 1
. 5 5.1 hexagon 2*sqrt(2)+8 8
. 5.2 octagon 4*sqrt(2)+8 14 a(5) = 1+2 = 3
. 6 pentagon 2*sqrt(2)+6 5 a(6) = 3+1 = 4
. 7 enneagon 6*sqrt(2)+6 13 a(7) = 4+1 = 5


CROSSREFS

Cf. A139250, A194270, A194271, A194277, A194278, A194444.
Sequence in context: A014615 A144046 A210934 * A184336 A183300 A155854
Adjacent sequences: A194273 A194274 A194275 * A194277 A194278 A194279


KEYWORD

nonn,hard,more


AUTHOR

Omar E. Pol, Aug 23 2011


STATUS

approved



