%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 like-fractal) 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.
%A _Omar E. Pol_, Aug 24 2011
%E More terms from _Omar E. Pol_, Mar 23 2013