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%I #29 Feb 22 2023 12:35:03
%S 0,1,3,7,11,15,23,34,42,46,54,70,94,106,126,151,167,171,179,195,219,
%T 247,283,325,369,389,413,453,517,549,593,646,678,682,690,706,730,758,
%U 794,838,890,932,980,1040,1140,1208,1292,1375,1459,1487,1511,1555
%N D-toothpick sequence of the second kind in the first quadrant.
%C This cellular automaton has essentially the same rules as A194270. We start at stage 0 with no toothpicks. At stage 1, we place a D-toothpick of length sqrt(2), in diagonal direction, at (0,0),(1,1). At stage 2, we place two toothpicks of length 1. At stage 3 we place four D-toothpicks. And so on. The toothpicks and D-toothpicks are connected by their endpoints. The sequence gives the number of toothpicks and D-toothpicks in the structure after n-th stage. The first differences (A194445) give the number of toothpicks or D-toothpicks added at n-th stage. It appears that the structure shows a fractal (or fractal-like) behavior.
%C First differs from A220524 at a(13). - _Omar E. Pol_, Mar 23 2013
%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>
%F a(n) = A194434(n)/4. - _Omar E. Pol_, Oct 15 2011
%Y Cf. A139250, A172310, A182838, A194270, A194432, A194434, A194440, A194442, A194445, A212008, A220524.
%K nonn
%O 0,3
%A _Omar E. Pol_, Aug 24 2011
%E More terms from _Omar E. Pol_, Mar 23 2013
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