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 A194276 Number of distinct polygonal shapes after n-th stage in the D-toothpick structure of A194270. 6
 0, 0, 0, 0, 1, 3, 4, 5, 6, 7, 9, 10, 10, 11, 13, 13, 14 (list; graph; refs; listen; history; text; internal format)
 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. 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.) - 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 N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS EXAMPLE Consider toothpicks of length 2 and D-toothpicks 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

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Last modified September 15 16:33 EDT 2019. Contains 327078 sequences. (Running on oeis4.)