%I
%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 Dtoothpick 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 Dtoothpick 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 Dtoothpicks. And so on. The toothpicks and Dtoothpicks are connected by their endpoints. The sequence gives the number of toothpicks and Dtoothpicks in the structure after nth stage. The first differences (A194445) give the number of toothpicks or Dtoothpicks added at nth stage. It appears that the structure shows a fractal (or likefractal) 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
