A182633 - OEIS

%I #21 Feb 24 2021 02:48:19

%S 0,3,6,12,12,12,24,36,24,12,24,48,60,48,60,84,48,12,24,48,60,60,84,

%T 132,132,72,60,120,168,144,156,192,96,12,24,48,60,60,84,132,132,84,84,

%U 156,228,228,228

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

%C First differences of A182632.

%C 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 David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a>

%H 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 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>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%F It appears that a(n) = 2*A161645(n) but with a(1)=3.

%F a(n) = 3*A182635(n). - _Omar E. Pol_, Feb 09 2013

%e From _Omar E. Pol_, Feb 08 2013 (Start):

%e When written as a triangle:

%e 0;

%e 3;

%e 6;

%e 12,12;

%e 12,24,36,24;

%e 12,24,48,60,48,60, 84, 48;

%e 12,24,48,60,60,84,132,132,72,60,120,168,144,156,192,96;

%e 12,24,48,60,60,84,132,132,84,84,156,228,228,228,...

%e ...

%e It appears that positive terms of the right border are A007283.

%e (End)

%Y A139250, A139251, A160120, A160121, A161206, A161207, A161644, A161645, A182632.

%K nonn,tabf,more

%O 0,2

%A _Omar E. Pol_, Dec 07 2010