A383369 Population of elementary triangular automaton rule 90 at generation n, starting from a lone 1 cell at generation 0.

1, 4, 6, 12, 6, 24, 24, 48, 6, 24, 36, 72, 24, 96, 96, 192, 6, 24, 36, 72, 36, 144, 144, 288, 24, 96, 144, 288, 96, 384, 384, 768, 6, 24, 36, 72, 36, 144, 144, 288, 36, 144, 216, 432, 144, 576, 576, 1152, 24, 96, 144, 288, 144, 576, 576, 1152, 96, 384, 576, 1152, 384, 1536, 1536, 3072, 6

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 90 (1011010 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|1|0|1|0|

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This is one of the 4 ETA rules (85, 90, 165 and 170) that replicates the pattern given as initial condition.

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 90

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.

Example

Written as an irregular triangle with row lengths A000079, starting from n=1, the sequence begins:
  4;
  6, 12;
  6, 24, 24, 48;
  6, 24, 36, 72, 24, 96, 96, 192;
  6, 24, 36, 72, 36, 144, 144, 288, 24, 96, 144, 288, 96, 384, 384, 768;
...
It appears that the right border gives A110594.

Crossrefs

Pattern replicating ETA rules: A275667 (rule 170).

A247640 is a bisection.

A246035 is the analog on the square cells.

Sequence in context: A078426 A212558 A293836 * A278252 A274298 A270835

Adjacent sequences: A383366 A383367 A383368 * A383370 A383371 A383372

Keyword

nonn

Author

Paul Cousin, Apr 24 2025

Status

approved