A253770 Number of ON states after n generations of cellular automaton based on triangles, with diamonds.

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

Offset

0,2

Comments

Also 6 times the Y-toothpicks sequence A160120.

Explanation: consider the Y-toothpick structure of A160120, then replace every Y-toothpick 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 n-th stage.

A253771 (the first differences) give the number of triangular cells turned "ON" at the n-th stage.

A160120 (the Y-toothpick sequence) gives the number of stars in the structure after the n-th stage.

A160121 gives the number of stars added at the n-th stage.

A160167 gives the number of diamonds in the structure after the n-th 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 A362803 A083212

Adjacent sequences: A253767 A253768 A253769 * A253771 A253772 A253773

Keyword

nonn

Author

Omar E. Pol, Jan 11 2015

Status

approved