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%I #23 Jun 14 2022 01:27:41
%S 1,6,29,123,503,2031,8159,32703,130943,524031,2096639,8387583,
%T 33552383,134213631,536862719,2147467263,8589901823,34359672831,
%U 137438822399,549755551743,2199022731263,8796091973631,35184369991679,140737484161023,562949945032703
%N Decimal representation of the n-th iteration of the "Rule 207" 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="/A267774/b267774.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 20 2016 and Apr 20 2019: (Start)
%F a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3) for n>3.
%F G.f.: (1-x+x^2-4*x^3) / ((1-x)*(1-2*x)*(1-4*x)).
%F (End)
%t rule=207; 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. A267773, A267775.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 20 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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