A384304 Population of elementary triangular automaton rule 86 at generation n, starting from a lone 1 cell at generation 0.

1, 4, 6, 18, 18, 39, 33, 69, 57, 111, 81, 123, 144, 195, 162, 252, 243, 306, 300, 336, 369, 414, 435, 495, 525, 603, 549, 693, 738, 807, 780, 933, 876, 1014, 1089, 1050, 1239, 1263, 1257, 1296, 1416, 1590, 1506, 1674, 1758, 1938, 1851, 1869, 1992, 2256, 2157

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 86 (1010110 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|1|0|1|0|1|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 86

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

Sequence in context: A309334 A263319 A062046 * A102020 A125133 A109310

Adjacent sequences: A384301 A384302 A384303 * A384305 A384306 A384307

Keyword

nonn

Author

Paul Cousin, May 25 2025

Status

approved