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A182633 Number of toothpicks added at n-th stage in the toothpick structure of A182632.

%I A182633 #21 Feb 24 2021 02:48:19
%S A182633 0,3,6,12,12,12,24,36,24,12,24,48,60,48,60,84,48,12,24,48,60,60,84,
%T A182633 132,132,72,60,120,168,144,156,192,96,12,24,48,60,60,84,132,132,84,84,
%U A182633 156,228,228,228
%N A182633 Number of toothpicks added at n-th stage in the toothpick structure of A182632.
%C A182633 First differences of A182632.
%C A182633 a(n) is also the number of components added at n-th stage in the toothpick structure formed by V-toothpicks with an initial Y-toothpick, since a V-toothpick has two components and a Y-toothpick has three components (For more information see A161206, A160120, A161644).
%H A182633 David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a>
%H A182633 David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
%H A182633 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 A182633 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%H A182633 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A182633 It appears that a(n) = 2*A161645(n) but with a(1)=3.
%F A182633 a(n) = 3*A182635(n). - _Omar E. Pol_, Feb 09 2013
%e A182633 From _Omar E. Pol_, Feb 08 2013 (Start):
%e A182633 When written as a triangle:
%e A182633 0;
%e A182633 3;
%e A182633 6;
%e A182633 12,12;
%e A182633 12,24,36,24;
%e A182633 12,24,48,60,48,60, 84, 48;
%e A182633 12,24,48,60,60,84,132,132,72,60,120,168,144,156,192,96;
%e A182633 12,24,48,60,60,84,132,132,84,84,156,228,228,228,...
%e A182633 ...
%e A182633 It appears that positive terms of the right border are A007283.
%e A182633 (End)
%Y A182633 A139250, A139251, A160120, A160121, A161206, A161207, A161644, A161645, A182632.
%K A182633 nonn,tabf,more
%O A182633 0,2
%A A182633 _Omar E. Pol_, Dec 07 2010