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A161644 Number of ON states after n generations of cellular automaton based on triangles. 13
0, 1, 4, 10, 16, 22, 34, 52, 64, 70, 82, 106, 136, 160, 190, 232, 256, 262, 274, 298, 328, 358, 400, 466, 532, 568, 598, 658, 742, 814, 892, 988, 1036, 1042, 1054, 1078, 1108, 1138, 1180, 1246, 1312, 1354, 1396, 1474, 1588, 1702, 1816, 1966, 2104, 2164, 2194 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Analog of A151723 and A151725, but here we are working on the hexagonal net where each triangular cell has three neighbors. A cell is turned ON if exactly one of its three neighbors is ON. An ON cell remains ON forever.

We start with a single ON cell.

It appears that a(n) is also the number of polytoothpicks added in a toothpick structure formed by V-toothpicks but starting with a Y-toothpick: a(n) = a(n-1)+(A182632(n)-A182632(n-1))/2. (Checked up to n=39.) - Omar E. Pol, Dec 07 2010 and R. J. Mathar, Dec 17 2010

It appears that the behavior is similar to A161206. - Omar E. Pol, Jan 15 2016

LINKS

Table of n, a(n) for n=0..50.

David Applegate, The movie version

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata

Lucas Garron, first 64 steps

Lucas Garron, after 128 steps

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

FORMULA

a(n) = (A182632(n) - 1)/2, n >= 1. - Omar E. Pol, Mar 07 2013

CROSSREFS

Cf. A151723, A151725, A147562, A161206, A161645, A139250, A160120, A161206, A182632, A182840, A250300.

Sequence in context: A269960 A016957 A109273 * A215032 A184527 A246297

Adjacent sequences:  A161641 A161642 A161643 * A161645 A161646 A161647

KEYWORD

nonn

AUTHOR

David Applegate and N. J. A. Sloane, Jun 15 2009

EXTENSIONS

Edited by N. J. A. Sloane, Jan 10 2010

STATUS

approved

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Last modified August 22 22:36 EDT 2017. Contains 290952 sequences.