A383417 Population of elementary triangular automaton rule 2 at generation n, starting from a lone 1 cell at generation 0.

1, 3, 6, 6, 12, 12, 18, 18, 30, 24, 48, 42, 54, 60, 72, 72, 90, 78, 114, 90, 120, 96, 162, 156, 162, 180, 282, 210, 306, 234, 300, 300, 342, 318, 378, 318, 378, 354, 384, 408, 408, 444, 600, 450, 612, 576, 654, 600, 726, 588, 798, 762, 786, 804, 924, 912, 984

Offset

0,2

Comments

An Elementary Triangular Automaton (ETA) is a cellular automaton in the triangular grid where cells hold binary states and rules are local to the first neighborhood. There are 256 possible ETA rules.

Rule 2 (10 in binary):

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|state of the cell |1|1|1|1|0|0|0|0|

|sum of the neighbors' states |3|2|1|0|3|2|1|0|

|cell's next state |0|0|0|0|0|0|1|0|

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This sequence also applies to rules 34, 66, 98, 130, 162, 194 and 226.

Links

Paul Cousin, Table of n, a(n) for n = 0..16384

Paul Cousin, Illustration for n = 0..128

Paul Cousin, Triangular Automata

Paul Cousin, Rule 2

Paul Cousin, Triangular Automata Integer Sequences

Paul Cousin, Triangular Automata: The 256 Elementary Cellular Automata of the Two-Dimensional Plane, Complex Systems, 33(3), 2024, pp. 253-276.

Crossrefs

Third center column of ETA rule 2: A383418.

Sequence in context: A232941 A080866 A310131 * A066393 A127777 A307204

Adjacent sequences: A383414 A383415 A383416 * A383418 A383419 A383420

Keyword

nonn

Author

Paul Cousin, Apr 26 2025

Status

approved