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

%I A383369 #20 May 14 2025 01:22:34
%S A383369 1,4,6,12,6,24,24,48,6,24,36,72,24,96,96,192,6,24,36,72,36,144,144,
%T A383369 288,24,96,144,288,96,384,384,768,6,24,36,72,36,144,144,288,36,144,
%U A383369 216,432,144,576,576,1152,24,96,144,288,144,576,576,1152,96,384,576,1152,384,1536,1536,3072,6
%N A383369 Population of elementary triangular automaton rule 90 at generation n, starting from a lone 1 cell at generation 0.
%C A383369 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.
%C A383369 Rule 90 (1011010 in binary):
%C A383369   -----------------------------------------------
%C A383369   |state of the cell            |1|1|1|1|0|0|0|0|
%C A383369   |sum of the neighbors' states |3|2|1|0|3|2|1|0|
%C A383369   |cell's next state            |0|1|0|1|1|0|1|0|
%C A383369   -----------------------------------------------
%C A383369 This is one of the 4 ETA rules (85, 90, 165 and 170) that replicates the pattern given as initial condition.
%H A383369 Paul Cousin, <a href="/A383369/b383369.txt">Table of n, a(n) for n = 0..16384</a>
%H A383369 Paul Cousin, <a href="/A383369/a383369.pdf">Illustration for n = 0..128</a>
%H A383369 Paul Cousin, <a href="https://triangular-automata.net">Triangular Automata</a>
%H A383369 Paul Cousin, <a href="https://triangular-automata.net/rules.html?rule=90">Rule 90</a>
%H A383369 Paul Cousin, <a href="https://triangular-automata.net/?p=integer-sequences">Triangular Automata Integer Sequences</a>
%H A383369 Paul Cousin, <a href="https://doi.org/10.25088/ComplexSystems.33.3.253">Triangular Automata: The 256 Elementary Cellular Automata of the Two-Dimensional Plane</a>, Complex Systems, 33(3), 2024, pp. 253-276.
%e A383369 Written as an irregular triangle with row lengths A000079, starting from n=1, the sequence begins:
%e A383369   4;
%e A383369   6, 12;
%e A383369   6, 24, 24, 48;
%e A383369   6, 24, 36, 72, 24, 96, 96, 192;
%e A383369   6, 24, 36, 72, 36, 144, 144, 288, 24, 96, 144, 288, 96, 384, 384, 768;
%e A383369 ...
%e A383369 It appears that the right border gives A110594.
%Y A383369 Pattern replicating ETA rules: A275667 (rule 170).
%Y A383369 A247640 is a bisection.
%Y A383369 A246035 is the analog on the square cells.
%K A383369 nonn
%O A383369 0,2
%A A383369 _Paul Cousin_, Apr 24 2025