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%I #17 Apr 18 2019 11:45:39
%S 1,1,10,75,76,1623,600,29295,4784,496351,37728,8164799,300736,
%T 132422527,2403712,2133112575,19192576,34244750847,153466368,
%U 548835613695,1227582464,8788730820607,9818265600,140678589542399,78541336576,2251328604004351,628321116160
%N Decimal 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="/A266674/b266674.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 -17*x^2 +40*x^3 -64*x^5 -248*x^6 +128*x^7 +1472*x^8 -2048*x^10) / ((1 -x)*(1 +x)*(1 -2*x)*(1 -4*x)*(1 +4*x)*(1 -2*x^2)*(1 +2*x +4*x^2)*(1 -8*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]],2],{k,1,rows}] (* Decimal Representation of Rows *)
%Y Cf. A266672.
%K nonn
%O 0,3
%A _Robert Price_, Jan 02 2016
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