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A194435 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A194434.

%I A194435 #44 Jun 30 2022 11:43:16
%S A194435 0,4,8,16,16,16,32,44,32,16,32,64,96,48,80,100,64,16,32,64,96,112,144,
%T A194435 168,176,80,96,160,256,128,176,212,128,16,32,64,96,112,144,176,208,
%U A194435 168,192,240,400,272,336,332,336,112,96,176,288,336,416,464
%N A194435 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A194434.
%C A194435 Essentially the first differences of A194434.
%C A194435 First differs from A221528 at a(13). - _Omar E. Pol_, Mar 23 2013
%C A194435 From _Omar E. Pol_, Jun 24 2022: (Start)
%C A194435 The word of this cellular automaton is "ab".
%C A194435 For the nonzero terms the structure of the irregular triangle is as shown below:
%C A194435   a,b;
%C A194435   a,b;
%C A194435   a,b,a,b;
%C A194435   a,b,a,b,a,b,a,b;
%C A194435   a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b;
%C A194435   ...
%C A194435 Row lengths are the terms of A011782 multiplied by 2, also the column 2 of A296612.
%C A194435 Columns "a" contain numbers of D-toothpicks (of length sqrt(2)).
%C A194435 Columns "b" contain numbers of toothpicks (of length 1).
%C A194435 An associated sound to the animation could be (tick, tock), (tick, tock), ..., the same as the ticking clock sound.
%C A194435 For further information about the word of cellular automata see A296612. (End)
%H A194435 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 A194435 Paolo Xausa, <a href="/A194434/a194434_1.gif">Animated version for n = 0..31</a> (red elements)
%H A194435 Paolo Xausa, <a href="/A194434/a194434_2.gif">Animated version for n = 0..63</a> (red elements)
%H A194435 Paolo Xausa, <a href="/A194434/a194434.pdf">Illustration of initial terms for n = 0..63</a> (red elements, multipage PDF)
%H A194435 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%F A194435 a(n) = 4*A194445(n).
%F A194435 Conjecture: a(2^k+1) = 16, if k >= 1.
%e A194435 From _Omar E. Pol_, Mar 23 2013: (Start)
%e A194435 When written as an irregular triangle the sequence of nonzeros terms begins:
%e A194435    4, 8;
%e A194435   16,16;
%e A194435   16,32,44,32;
%e A194435   16,32,64,96, 48, 80,100, 64;
%e A194435   16,32,64,96,112,144,168,176, 80, 96,160,256,128,176,212,128;
%e A194435   16,32,64,96,112,144,176,208,168,192,240,400,272,336,332,336,112,96, ...
%e A194435   ... (End)
%e A194435 Right border gives the powers of 2 >= 8 (reformatted the triangle). - _Omar E. Pol_, Jun 24 2022
%Y A194435 Cf. A011782, A139251, A194271, A194433, A194434, A194441, A194443, A194445, A212009, A221528, A299612.
%K A194435 nonn,tabf
%O A194435 0,2
%A A194435 _Omar E. Pol_, Sep 03 2011
%E A194435 More terms from _Omar E. Pol_, Mar 23 2013