%I
%S 4,8,8,12,4,32,16,64,36,72,52,124,88,144,108,192,132,212,152,
%T 248,140,284,268,392,348,396,220,276,68,180,160,328,164,372,
%U 304,392,176,316,204,396,220,496,492,720,304,320,248,488,252,444
%N First differences of number of active (ON,black) cells in nth stage of growth of twodimensional cellular automaton defined by "Rule 542", based on the 5celled von Neumann neighborhood.
%C Initialized with a single black (ON) cell at stage zero.
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H Robert Price, <a href="/A272812/b272812.txt">Table of n, a(n) for n = 0..127</a>
%H N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015
%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_2D_5Neighbor_Cellular_Automata">Index to 2D 5Neighbor Cellular Automata</a>
%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t CAStep[rule_,a_]:=Map[rule[[10#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];
%t code=542; stages=128;
%t rule=IntegerDigits[code,2,10];
%t g=2*stages+1; (* Maximum size of grid *)
%t a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *)
%t ca=a;
%t ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}];
%t PrependTo[ca,a];
%t (* Trim full grid to reflect growth by one cell at each stage *)
%t k=(Length[ca[[1]]]+1)/2;
%t ca=Table[Table[Part[ca[[n]][[j]],Range[k+1n,k1+n]],{j,k+1n,k1+n}],{n,1,k}];
%t on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%t Table[on[[i+1]]on[[i]],{i,1,Length[on]1}] (* Difference at each stage *)
%Y Cf. A272809.
%K sign,easy
%O 0,1
%A _Robert Price_, May 06 2016
