A160167 Total number of single toothpicks after n-th stage in the Y-toothpick structure of A160120.

0, 3, 12, 21, 48, 57, 84, 111, 174, 201, 228, 255, 318, 363, 426, 507, 660, 741, 768, 795, 858, 903, 966, 1047, 1200, 1299, 1362, 1443, 1596, 1749, 1920, 2127, 2478, 2721, 2784, 2811, 2874, 2919, 2982, 3063, 3216, 3315, 3378, 3459, 3612, 3765, 3936, 4143, 4494, 4755, 4854, 4935

Offset

0,2

Comments

Also, replace the Y-toothpick with the "three-diamonds" symbol, so we have a new cellular automaton in which a(n) counts the total number of diamonds in the structure after the n-th stage, A160120 also gives the total number of "three-diamonds" symbols after the n-th stage, and A253770 gives the total number of triangular ON cells after the n-th stage. - Omar E. Pol, Feb 10 2015

Links

Table of n, a(n) for n=0..51.

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

Formula

a(n) = 3*A160120(n).

a(n) = 3*A160157(n)/2 = A253770(n)/2. - Omar E. Pol, Feb 10 2015

Example

From Omar E. Pol, Feb 10 2015: (Start)
After one generation, also, the cellular automaton looks like a star or a flower with three petals as shown below:
.
.        /\
.       _\/_
.      /_/\_\
.
There are six ON cells and three diamonds, so a(1) = 3.
(End)

Crossrefs

Cf. A139250, A160120, A160157, A253770.

Sequence in context: A119507 A044436 A210282 * A160412 A091846 A061262

Adjacent sequences: A160164 A160165 A160166 * A160168 A160169 A160170

Keyword

nonn

Author

Omar E. Pol, Jun 01 2009, Jun 09 2009

Extensions

New name and more terms from Omar E. Pol, Feb 10 2015

Status

approved