%I #9 Apr 29 2016 11:24:09
%S 1,5,14,46,67,167,208,372,445,741,842,1278,1415,2039,2236,2960,3261,
%T 4269,4534,5874,6203,7863,8200,10080,10549,12849,13426,16078,16759,
%U 19847,20596,23812,24929,28717,29734,34098,35251,40351,41312,46852,48101,54153,55650
%N Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 473", based on the 5-celled 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="/A272425/b272425.txt">Table of n, a(n) for n = 0..128</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_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor 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=473; 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+1-n,k-1+n]],{j,k+1-n,k-1+n}],{n,1,k}];
%t on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%t Table[Total[Part[on,Range[1,i]]],{i,1,Length[on]}] (* Sum at each stage *)
%Y Cf. A272423.
%K nonn,easy
%O 0,2
%A _Robert Price_, Apr 29 2016
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