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%I #19 Apr 18 2019 11:45:12
%S 1,1,1010,1001011,1001100,11001010111,1001011000,111001001101111,
%T 1001010110000,1111001001011011111,1001001101100000,
%U 11111001001010110111111,1001001011011000000,111111001001001101101111111,1001001010110110000000,1111111001001001011011011111111
%N Binary representation of the n-th iteration of the "Rule 57" 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="/A266673/b266673.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 Empirical g.f.: (1 +x -10001*x^2 +989000*x^3 -1000000*x^5 -899991000*x^6 +10000000*x^7 +10911000000*x^8 -20000000000*x^10) / ((1 -x)*(1 +x)*(1 -10*x)*(1 -100*x)*(1 +100*x)*(1 -10*x^2)*(1 +10*x +100*x^2)*(1 -1000*x^2)). - _Colin Barker_, Jan 03 2016 and Apr 18 2019
%t rule=57; 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]]],{k,1,rows}] (* Binary Representation of Rows *)
%Y Cf. A266672.
%K nonn
%O 0,3
%A _Robert Price_, Jan 02 2016