A384355 Population of elementary triangular automaton rule 58 at generation n, starting from a lone 1 cell at generation 0.

1, 4, 9, 13, 22, 18, 36, 54, 48, 54, 84, 96, 108, 132, 180, 204, 174, 186, 252, 216, 294, 258, 264, 432, 324, 426, 474, 534, 498, 702, 666, 732, 648, 792, 750, 816, 834, 864, 840, 942, 852, 1068, 972, 1218, 1080, 1272, 1392, 1572, 1506, 1380, 1728, 1716, 1662

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 58 (111010 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|1|1|1|0|1|0|

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Links

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

Paul Cousin, Illustration for n = 0..64

Paul Cousin, Triangular Automata

Paul Cousin, Rule 58

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

Slice of ETA rule 58: A384363.

Sequence in context: A312986 A240692 A345743 * A022130 A042125 A041905

Adjacent sequences: A384352 A384353 A384354 * A384356 A384357 A384358

Keyword

nonn

Author

Paul Cousin, May 27 2025

Status

approved