A182633 - OEIS

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A182633

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

0, 3, 6, 12, 12, 12, 24, 36, 24, 12, 24, 48, 60, 48, 60, 84, 48, 12, 24, 48, 60, 60, 84, 132, 132, 72, 60, 120, 168, 144, 156, 192, 96, 12, 24, 48, 60, 60, 84, 132, 132, 84, 84, 156, 228, 228, 228

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

First differences of A182632.

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).

LINKS

Table of n, a(n) for n=0..46.

David Applegate, The movie version

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, 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.]

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to toothpick sequences

Index entries for sequences related to cellular automata

FORMULA

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

a(n) = 3*A182635(n). - Omar E. Pol, Feb 09 2013

EXAMPLE

From Omar E. Pol, Feb 08 2013 (Start):

When written as a triangle:

12,12;

12,24,36,24;

12,24,48,60,48,60, 84, 48;