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A267359 Binary representation of the n-th iteration of the "Rule 125" elementary cellular automaton starting with a single ON (black) cell. 2

%I #29 Jul 06 2023 13:16:19

%S 1,11,11100,101111,111110000,1000111111,1111101000000,10001111111111,

%T 11111010000000000,100011111111111111,111110100000000000000,

%U 1000111111111111111111,1111101000000000000000000,10001111111111111111111111,11111010000000000000000000000

%N Binary representation of the n-th iteration of the "Rule 125" elementary cellular automaton starting with a single ON (black) cell.

%H Robert Price, <a href="/A267359/b267359.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 and Apr 19 2019: (Start)

%F a(n) = 10001*a(n-2) - 10000*a(n-4) for n > 8.

%F G.f.: (1 + 11*x + 1099*x^2 - 8900*x^3 + 108900*x^4 - 10990000*x^5 + 890000*x^6 + 11000000*x^7 - 1000000*x^8) / ((1 - x)*(1 + x)*(1 - 100*x)*(1 + 100*x)).

%F (End)

%t rule=125; 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. A267358, A267360.

%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 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)