

A253770


Number of ON states after n generations of cellular automaton based on triangles, with diamonds.


4



0, 6, 24, 42, 96, 114, 168, 222, 348, 402, 456, 510, 636, 726, 852, 1014, 1320, 1482, 1536, 1590, 1716, 1806, 1932, 2094, 2400, 2598, 2724, 2886, 3192, 3498, 3840, 4254, 4956, 5442, 5568, 5622, 5748, 5838, 5964, 6126, 6432, 6630, 6756, 6918, 7224, 7530, 7872, 8286
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Also 6 times the Ytoothpicks sequence A160120.
Explanation: consider the Ytoothpick structure of A160120, then replace every Ytoothpick with six ON cells forming a star with three rhombuses (or diamonds) that share only one vertex. Every diamond contains two triangular cells that share one edge.
The rules are the essentially the same as A160120.
An ON cell remains ON forever.
The sequence gives the number of triangular ON cells after the nth stage.
A253771 (the first differences) give the number of triangular cells turned "ON" at the nth stage.
A160120 (the Ytoothpick sequence) gives the number of stars in the structure after the nth stage.
A160121 gives the number of stars added at the nth stage.
A160167 gives the number of diamonds in the structure after the nth stage.


LINKS

Table of n, a(n) for n=0..47.
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to cellular automata


FORMULA

a(n) = 6*A160120(n) = 3*A160157(n) = 2*A160167(n).


EXAMPLE

After one generation, the cellular automaton looks like a star or a flower with three petals as shown below:
.
. /\
. _\/_
. /_/\_\
.
There are one star, three diamonds and six ON cells, so a(1) = 6.


CROSSREFS

Cf. A139250, A147562, A151723, A160120, A160157, A160167, A161644, A182632, A250300, A253771.
Sequence in context: A069541 A062768 A161333 * A002688 A083212 A120572
Adjacent sequences: A253767 A253768 A253769 * A253771 A253772 A253773


KEYWORD

nonn


AUTHOR

Omar E. Pol, Jan 11 2015


STATUS

approved



