A384363 Slice of elementary triangular automaton rule 58, starting from a lone 1 cell.

1, 3, 6, 13, 31, 48, 104, 220, 484, 796, 1700, 3580, 7940, 12588, 27516, 57284, 122956, 201036, 439756, 909068, 2048428, 3260604, 6950308, 14619132, 31505156, 51481228, 112237244, 232238020, 525920332, 837265868, 1779497548, 3753480012, 8055847244, 13161451340

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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This is the sequence of numbers formed in binary by the states that start at the initial 1 cell and follow a direction parallel to any of its sides.

Links

Paul Cousin, Table of n, a(n) for n = 0..2048

Paul Cousin, Illustration for n = 0..64

Paul Cousin, Sequence plot for n = 0..8192 (binary digits, left-to-right)

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

Population of ETA rule 58: A384355.

Sequence in context: A141353 A130582 A126296 * A293911 A018014 A358937

Adjacent sequences: A384360 A384361 A384362 * A384364 A384365 A384366

Keyword

nonn

Author

Paul Cousin, May 27 2025

Status

approved