A379341 Population of elementary triangular automaton rule 50 at generation n, starting from a lone 1 cell at generation 0.

1, 4, 9, 12, 18, 24, 36, 48, 54, 60, 84, 90, 108, 126, 162, 180, 186, 192, 216, 222, 252, 270, 330, 360, 390, 396, 480, 486, 552, 582, 690, 696, 702, 708, 732, 738, 768, 786, 846, 876, 918, 924, 1044, 1050, 1140, 1194, 1350, 1404, 1434, 1440, 1524, 1530, 1632

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 50 (110010 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|0|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..128

Paul Cousin, Triangular Automata

Paul Cousin, Rule 50

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: A319745 A312865 A376340 * A348918 A181023 A084789

Adjacent sequences: A379338 A379339 A379340 * A379342 A379343 A379344

Keyword

nonn

Author

Paul Cousin, May 23 2025

Status

approved