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A267350 Binary representation of the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell. 2

%I #30 Jul 06 2023 13:15:07

%S 1,101,1110,1110111,111000,11111011111,11100000,111111101111111,

%T 1110000000,1111111110111111111,111000000000,11111111111011111111111,

%U 11100000000000,111111111111101111111111111,1110000000000000,1111111111111110111111111111111,111000000000000000

%N Binary representation of the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell.

%H Robert Price, <a href="/A267350/b267350.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>

%H Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%F Conjectures from _Colin Barker_, Jan 14 2016: (Start)

%F a(n) = 10101*a(n-2) - 1010100*a(n-4) + 1000000*a(n-6) for n > 6.

%F G.f.: (1 + 101*x - 8991*x^2 + 89910*x^3 - 10091010*x^4 - 200000*x^5 + 10100000*x^6) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).

%F (End)

%t rule=123; rows=20; ca=CellularAutomaton[rule,{{1},0},rows-1,{All,All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]],{rows-k+1,rows+k-1}],{k,1,rows}]; (* truncated list of each row *) Table[FromDigits[catri[[k]]],{k,1,rows}] (* binary representation of rows *)

%Y Cf. A267349, A267351.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 13 2016

%E Removed an unjustified claim that _Colin Barker_'s conjectures are correct. Removed a program based on a conjecture. - _Michael De Vlieger_, Jun 13 2022

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Last modified March 28 07:48 EDT 2024. Contains 371235 sequences. (Running on oeis4.)