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%I #33 Jul 06 2023 13:24:00
%S 1,1,11,47,191,767,3071,12287,49151,196607,786431,3145727,12582911,
%T 50331647,201326591,805306367,3221225471,12884901887,51539607551,
%U 206158430207,824633720831,3298534883327,13194139533311,52776558133247,211106232532991,844424930131967
%N Decimal representation of the n-th iteration of the "Rule 185" 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="/A267614/b267614.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 18 2016 and Apr 20 2019: (Start)
%F a(n) = 5*a(n-1) - 4*a(n-2) for n>3.
%F G.f.: (1-4*x+10*x^2-4*x^3) / ((1-x)*(1-4*x)).
%F (End)
%F Empirical a(n) = 3*4^(n-1)-1 for n>1. - _Colin Barker_, Nov 25 2016 and Apr 20 2019
%t rule=185; 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. A198693, A267612, A267613.
%K nonn,easy
%O 0,3
%A _Robert Price_, Jan 18 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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