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A256266 Total number of ON states after n generations of cellular automaton based on triangles (see Comments lines for definition). 3
0, 6, 18, 24, 48, 66, 78, 84, 132, 174, 210, 240, 264, 282, 294, 300, 396, 486, 570, 648, 720, 786, 846, 900, 948, 990, 1026, 1056, 1080, 1098, 1110, 1116, 1308, 1494, 1674, 1848, 2016, 2178, 2334, 2484, 2628, 2766, 2898, 3024, 3144, 3258, 3366, 3468, 3564, 3654, 3738, 3816, 3888, 3954, 4014, 4068, 4116, 4158, 4194, 4224, 4248 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

On the infinite triangular grid we start at stage 0 with a hexagon formed by six OFF cells, so a(0) = 0.

At stage 1, around the mentioned hexagon, six triangular cells connected by their vertices are turned ON forming a six-pointed star, so a(1) = 6.

We use the same rules as A255748 for every one of the six 60-degree wedges of the structure.

If n is a power of 2 minus 1 and n is greater than 2, then the structure looks like concentric six-pointed stars.

If n is a power of 2 and n is greater than 2, then the structure looks like a hexagon that contains concentric six-pointed stars.

Note that in every wedge the structure seems to grow into the holes of a virtual Sierpiński's triangle (see example).

LINKS

Table of n, a(n) for n=0..60.

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 * A255748(n), n >= 1.

EXAMPLE

Illustration of the structure after 15 generations:

(Note that every circle should be replaced with a triangle.)

.

.                            O

.                           O O

.                          O O O

.                         O O O O

.                        O O O O O

.                       O O O O O O

.                      O O O O O O O

.                     O O O O O O O O

.    O O O O O O O O \       O       / O O O O O O O O

.     O O O O O O O   \     O O     /   O O O O O O O

.      O O O O O O     \   O O O   /     O O O O O O

.       O O O O O       \ O O O O /       O O O O O

.        O O O O O O O O \   O   / O O O O O O O O

.         O O O   O O O   \ O O /   O O O   O O O

.          O O     O O O O \ O / O O O O     O O

.           O       O   O O \ / O O   O       O

.            - - - - - - - -   - - - - - - - -

.           O       O   O O / \ O O   O       O

.          O O     O O O O / O \ O O O O     O O

.         O O O   O O O   / O O \   O O O   O O O

.        O O O O O O O O /   O   \ O O O O O O O O

.       O O O O O       / O O O O \       O O O O O

.      O O O O O O     /   O O O   \     O O O O O O

.     O O O O O O O   /     O O     \   O O O O O O O

.    O O O O O O O O /       O       \ O O O O O O O O

.                     O O O O O O O O

.                      O O O O O O O

.                       O O O O O O

.                        O O O O O

.                         O O O O

.                          O O O

.                           O O

.                            O

.

There are 300 ON cells, so a(15) = 300.

CROSSREFS

Cf. A001316, A047999, A080079, A139250, A151723, A160120, A161330, A161644, A255748, A256256.

Sequence in context: A283118 A274536 A051395 * A228104 A028558 A140450

Adjacent sequences:  A256263 A256264 A256265 * A256267 A256268 A256269

KEYWORD

nonn,look

AUTHOR

Omar E. Pol, Mar 20 2015

STATUS

approved

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Last modified December 19 03:45 EST 2018. Contains 318245 sequences. (Running on oeis4.)