# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a271003
Showing 1-1 of 1

%I A271003 #9 Jul 26 2024 21:16:35
%S A271003 4,4,32,-20,80,-52,136,-124,248,-212,352,-324,508,-432,628,-652,940,
%T A271003 -912,1240,-1264,1500,-1296,1540,-1488,1900,-1872,2252,-2196,2620,
%U A271003 -2376,2700,-2736,3388,-3444,4024,-3936,4356,-4104,4600,-4680,5404,-5204,5664,-5452
%N A271003 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 243", based on the 5-celled von Neumann neighborhood.
%C A271003 Initialized with a single black (ON) cell at stage zero.
%D A271003 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A271003 Robert Price, <a href="/A271003/b271003.txt">Table of n, a(n) for n = 0..127</a>
%H A271003 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 A271003 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A271003 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A271003 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A271003 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A271003 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A271003 CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];
%t A271003 code=243; stages=128;
%t A271003 rule=IntegerDigits[code,2,10];
%t A271003 g=2*stages+1; (* Maximum size of grid *)
%t A271003 a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *)
%t A271003 ca=a;
%t A271003 ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}];
%t A271003 PrependTo[ca,a];
%t A271003 (* Trim full grid to reflect growth by one cell at each stage *)
%t A271003 k=(Length[ca[[1]]]+1)/2;
%t A271003 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 A271003 on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%t A271003 Table[on[[i+1]]-on[[i]],{i,1,Length[on]-1}] (* Difference at each stage *)
%Y A271003 Cf. A269702.
%K A271003 sign,easy
%O A271003 0,1
%A A271003 _Robert Price_, Mar 28 2016

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE