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%I #19 Apr 20 2019 06:16:47
%S 1,3,27,123,507,2043,8187,32763,131067,524283,2097147,8388603,
%T 33554427,134217723,536870907,2147483643,8589934587,34359738363,
%U 137438953467,549755813883,2199023255547,8796093022203,35184372088827,140737488355323,562949953421307
%N Decimal representation of the n-th iteration of the "Rule 245" 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="/A267924/b267924.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 23 2016 and Apr 20 2019: (Start)
%F a(n) = 5*a(n-1)-4*a(n-2) for n>2.
%F G.f.: (1-2*x+16*x^2) / ((1-x)*(1-4*x)).
%F (End)
%F Empirical a(n) = 2^(2*n+1) - 5 for n>0. - _Colin Barker_, Nov 26 2016 and Apr 20 2019
%t rule=245; 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. A267922.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 22 2016
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