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A272312 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 462", based on the 5-celled von Neumann neighborhood.

%I A272312 #10 Feb 16 2025 08:33:33
%S A272312 4,3,13,-1,12,16,17,-9,28,0,28,24,60,20,81,-53,56,8,-40,88,40,72,104,
%T A272312 -48,20,72,128,52,104,60,185,-133,72,-32,68,68,80,208,116,76,-48,164,
%U A272312 -8,84,180,104,360,-20,-68,56,136,-36,260,176,284,-120,212,76,64
%N A272312 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 462", based on the 5-celled von Neumann neighborhood.
%C A272312 Initialized with a single black (ON) cell at stage zero.
%D A272312 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A272312 Robert Price, <a href="/A272312/b272312.txt">Table of n, a(n) for n = 0..127</a>
%H A272312 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 A272312 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A272312 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A272312 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A272312 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A272312 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A272312 CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];
%t A272312 code=462; stages=128;
%t A272312 rule=IntegerDigits[code,2,10];
%t A272312 g=2*stages+1; (* Maximum size of grid *)
%t A272312 a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *)
%t A272312 ca=a;
%t A272312 ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}];
%t A272312 PrependTo[ca,a];
%t A272312 (* Trim full grid to reflect growth by one cell at each stage *)
%t A272312 k=(Length[ca[[1]]]+1)/2;
%t A272312 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 A272312 on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%t A272312 Table[on[[i+1]]-on[[i]],{i,1,Length[on]-1}] (* Difference at each stage *)
%Y A272312 Cf. A246330.
%K A272312 sign,easy
%O A272312 0,1
%A A272312 _Robert Price_, Apr 25 2016