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%I #21 Jun 13 2022 21:27:53
%S 1,3,7,11,23,43,87,171,343,683,1367,2731,5463,10923,21847,43691,87383,
%T 174763,349527,699051,1398103,2796203,5592407,11184811,22369623,
%U 44739243,89478487,178956971,357913943,715827883,1431655767,2863311531,5726623063,11453246123
%N Decimal representation of the n-th iteration of the "Rule 92" elementary cellular automaton starting with a single ON (black) cell.
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H Robert Price, <a href="/A267052/b267052.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 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%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 10 2016 and Apr 17 2019: (Start)
%F a(n) = (3+2*(-1)^n+2^(2+n))/3 for n>0.
%F a(n) = 2*a(n-1)+a(n-2)-2*a(n-3) for n>3.
%F G.f.: (1+x-4*x^3) / ((1-x)*(1+x)*(1-2*x)).
%F (End)
%t rule=92; 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]],2],{k,1,rows}] (* Decimal Representation of Rows *)
%Y Cf. A267050, A267051.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 09 2016
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