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%I A194276 #67 Nov 08 2017 09:03:20
%S A194276 0,0,0,0,1,3,4,5,6,7,9,10,10,11,13,13,14
%N A194276 Number of distinct polygonal shapes after n-th stage in the D-toothpick structure of A194270.
%C A194276 The cellular automaton of A194270 contains a large number of distinct polygonal shapes. For simplicity we also call polygonal shapes "polygons".
%C A194276 In order to construct this sequence we use the following rules:
%C A194276 - Consider only the convex polygons and the concave polygons. Self-intersecting polygons are not counted. (Note that some polygons contain in their body a toothpick or D-toothpick with an exposed endpoint; that element is not a part of the perimeter of the polygon.)
%C A194276 - If two polygons have the same shape but they have different size then these polygons must be counted as distinct polygonal shapes.
%C A194276 - The reflected shapes of asymmetric polygons, both with the same area, must be counted as distinct polygonal shapes.
%C A194276 For more information see A194277 and A194278.
%C A194276 Question: Is there a maximal record in this sequence?
%H A194276 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 A194276 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%e A194276 Consider toothpicks of length 2 and D-toothpicks of length sqrt(2).
%e A194276 .
%e A194276 Stage       New type  Perimeter    Area   Term       a(n)
%e A194276 . 0            -          -          -    a(0) =       0
%e A194276 . 1            -          -          -    a(1) =       0
%e A194276 . 2            -          -          -    a(2) =       0
%e A194276 . 3            -          -          -    a(3) =       0
%e A194276 . 4         hexagon   4*sqrt(2)+4    6    a(4) =       1
%e A194276 . 5   5.1   hexagon   2*sqrt(2)+8    8
%e A194276 .     5.2   octagon   4*sqrt(2)+8   14    a(5) = 1+2 = 3
%e A194276 . 6         pentagon  2*sqrt(2)+6    5    a(6) = 3+1 = 4
%e A194276 . 7         enneagon  6*sqrt(2)+6   13    a(7) = 4+1 = 5
%Y A194276 Cf. A139250, A194270, A194271, A194277, A194278, A194444.
%K A194276 nonn,hard,more
%O A194276 0,6
%A A194276 _Omar E. Pol_, Aug 23 2011

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