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%I #50 Feb 22 2023 08:02:56
%S 0,4,12,28,44,60,92,136,168,184,216,280,376,424,504,604,668,684,716,
%T 780,876,988,1132,1300,1476,1556,1652,1812,2068,2196,2372,2584,2712,
%U 2728,2760,2824,2920,3032,3176,3352,3560,3728,3920,4160,4560,4832,5168
%N D-toothpick sequence of the second kind starting with a X-shaped cross formed by 4 D-toothpicks.
%C On the infinite square grid we start with no toothpicks.
%C At stage 1, we place a cross as a "X", formed by 4 D-toothpicks of length sqrt(2) and centered at the origin. At stage 2, we place 8 toothpicks of length 1. At stage 3, we place 16 D-toothpicks of length sqrt(2). And so on.
%C The sequence gives the number of toothpicks and D-toothpicks in the structure after n-th stage. The first differences (A194435) give the number of toothpicks or D-toothpicks added at n-th stage.
%C Apparently this cellular automaton has a fractal behavior (or fractal-like behavior) related to power of 2, similar to A194270 and very similar to A194432. The octagonal structure contains a large number of distinct closed polygonal regions. For more information see A194270, A194440 and A194442.
%C First differs from A220514 at a(13). - _Omar E. Pol_, Mar 23 2013
%C Observation: at least for the terms in the Data section the graph also appears to be a companion of the graph of A187210 but that could be different comparing more terms. - _Omar E. Pol_, Jun 24 2022
%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 Paolo Xausa, <a href="/A194434/a194434_1.gif">Animated version for n = 0..31</a>
%H Paolo Xausa, <a href="/A194434/a194434_2.gif">Animated version for n = 0..63</a>
%H Paolo Xausa, <a href="/A194434/a194434.pdf">Illustration of initial terms for n = 0..63</a> (multipage PDF)
%H <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%F a(n) = 4*A194444(n).
%Y Cf. A139250, A187210, A194270, A194432, A194435, A194440, A194442, A194444, A212008, A220514.
%K nonn
%O 0,2
%A _Omar E. Pol_, Sep 03 2011
%E More terms from _Omar E. Pol_, Mar 23 2013
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