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A267941 Decimal representation of the n-th iteration of the "Rule 253" elementary cellular automaton starting with a single ON (black) cell.

%I A267941 #22 Feb 16 2025 08:33:30
%S A267941 1,3,31,127,511,2047,8191,32767,131071,524287,2097151,8388607,
%T A267941 33554431,134217727,536870911,2147483647,8589934591,34359738367,
%U A267941 137438953471,549755813887,2199023255551,8796093022207,35184372088831,140737488355327,562949953421311
%N A267941 Decimal representation of the n-th iteration of the "Rule 253" elementary cellular automaton starting with a single ON (black) cell.
%C A267941 With the exception of a(1) the same as A267938, A267890, A267888 and A083420. - _R. J. Mathar_, Jan 24 2016
%D A267941 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A267941 Robert Price, <a href="/A267941/b267941.txt">Table of n, a(n) for n = 0..1000</a>
%H A267941 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267941 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A267941 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267941 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A267941 Conjectures from _Colin Barker_, Jan 23 2016 and Apr 16 2019: (Start)
%F A267941 a(n) = 5*a(n-1)-4*a(n-2) for n>3.
%F A267941 G.f.: (1-2*x+20*x^2-16*x^3) / ((1-x)*(1-4*x)).
%F A267941 (End)
%F A267941 Empirical a(n) = 2^(2*n+1) - 1 for n>1. - _Colin Barker_, Nov 26 2016
%t A267941 rule=253; 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 A267941 Cf. A060576.
%K A267941 nonn,easy
%O A267941 0,2
%A A267941 _Robert Price_, Jan 22 2016