%I #17 Apr 16 2019 11:32:51

%S 1,5,29,125,509,2045,8189,32765,131069,524285,2097149,8388605,

%T 33554429,134217725,536870909,2147483645,8589934589,34359738365,

%U 137438953469,549755813885,2199023255549,8796093022205,35184372088829,140737488355325,562949953421309

%N Decimal representation of the n-th iteration of the "Rule 243" 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="/A267921/b267921.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 22 2016 and Apr 16 2019: (Start)

%F a(n) = 5*a(n-1)-4*a(n-2) for n>2.

%F G.f.: (1+8*x^2) / ((1-x)*(1-4*x)).

%F (End)

%F Empirical a(n) = 2^(2*n+1) - 3 for n>0. - _Colin Barker_, Nov 25 2016

%t rule=243; 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. A267919.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 22 2016