This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%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