%N D-toothpick sequence starting with a cross formed by 4 toothpicks.
%C On the infinite square grid we start with no toothpicks.
%C At stage 1, we place a cross, centered at the origin, formed by 2 vertical toothpicks and 2 horizontal toothpicks of length 1. At stage 2, we place 8 D-toothpicks of length sqrt(2). At stage 3, we place 16 toothpicks of length 1. And so on.
%C The sequence gives the number of toothpicks and D-toothpicks in the structure after n-th stage. The first differences (A194433) give the number of toothpicks and D-toothpicks added at n-th stage.
%C Apparently this cellular automaton has a fractal behavior (or like-fractal behavior) related to power of 2, similar to A194270 and very similar to A194434. The octagonal structure contains a large number of distinct polygonal shapes. For more information see A194270, A194440 and A194442.
%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, A194270, A194433, A194434, A194440, A194442.
%A _Omar E. Pol_, Sep 03 2011