A380012 Population of elementary triangular automaton rule 54 at generation n, starting from a lone 1 cell at generation 0.

1, 4, 9, 15, 21, 36, 36, 57, 66, 87, 81, 129, 129, 162, 162, 225, 228, 270, 267, 351, 324, 342, 483, 411, 468, 516, 588, 639, 600, 723, 762, 777, 795, 960, 888, 1071, 972, 1056, 1323, 1158, 1242, 1362, 1362, 1557, 1449, 1689, 1677, 1845, 1710, 1977, 2007, 2100, 2166, 2178, 2499, 2409, 2430, 2556

Offset: 0

Author

Paul Cousin, Jan 09 2025

Keywords

• nonn

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 54 (110110 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|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 54
• 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

Second center column of ETA rule 54 from a lone 1 cell: A380172.

Third center column of ETA rule 54 from a lone 1 cell: A380173.