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

Author

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

Keywords

• nonn

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

Examples

			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)
		

Links

• 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

Crossrefs

Cf. A139250, A160120, A160157, A253770.

Formula

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

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

Extensions

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