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%I #26 Jul 06 2023 13:18:07
%S 1,2,4,8,84,168,1364,2728,21844,43688,349524,699048,5592404,11184808,
%T 89478484,178956968,1431655764,2863311528,22906492244,45812984488,
%U 366503875924,733007751848,5864062014804,11728124029608,93824992236884,187649984473768
%N Decimal representation of the n-th iteration of the "Rule 133" elementary cellular automaton starting with a single ON (black) cell.
%H Robert Price, <a href="/A267457/b267457.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 15 2016 and Apr 19 2019: (Start)
%F a(n) = 17*a(n-2)-16*a(n-4) for n>5.
%F G.f.: (1+2*x)*(1-13*x^2+32*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
%F (End)
%t rule=133; 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. A267423, A267456.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 15 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