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%I #30 Jul 06 2023 13:10:06
%S 1,101,1000,1101111,1000000,11101111111,1000000000,111101111111111,
%T 1000000000000,1111101111111111111,1000000000000000,
%U 11111101111111111111111,1000000000000000000,111111101111111111111111111,1000000000000000000000,1111111101111111111111111111111
%N Binary representation of the n-th iteration of the "Rule 83" elementary cellular automaton starting with a single ON (black) cell.
%H Robert Price, <a href="/A267002/b267002.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 08 2016 and Apr 19 2019: (Start)
%F a(n) = 11001*a(n-2)-10011000*a(n-4)+10000000*a(n-6) for n>5.
%F G.f.: (1+101*x-10001*x^2-9990*x^3+10000*x^4-1100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-1000*x^2)).
%F (End)
%t rule=83; 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. A267001, A267003.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 08 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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