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A273911 Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 614", based on the 5-celled von Neumann neighborhood.

%I A273911 #12 May 25 2025 22:35:43
%S A273911 1,3,5,11,17,55,69,219,257,775,1301,2923,4113,12407,20805,46811,65537,
%T A273911 196615,327701,721003,1114385,3606391,4527173,14380507,16777473,
%U A273911 50333447,83891477,184576875,285282321,923234423,1158959429,3681400539,4294967297,12884901895
%N A273911 Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 614", based on the 5-celled von Neumann neighborhood.
%C A273911 Initialized with a single black (ON) cell at stage zero.
%D A273911 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A273911 Robert Price, <a href="/A273911/b273911.txt">Table of n, a(n) for n = 0..126</a>
%H A273911 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 A273911 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A273911 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A273911 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A273911 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A273911 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A273911 a(n) = Sum_{k=0..n} 2^k*(A383609(n, k) mod 2). - _Mélika Tebni_, May 16 2025
%t A273911 CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];
%t A273911 code=614; stages=128;
%t A273911 rule=IntegerDigits[code,2,10];
%t A273911 g=2*stages+1; (* Maximum size of grid *)
%t A273911 a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *)
%t A273911 ca=a;
%t A273911 ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}];
%t A273911 PrependTo[ca,a];
%t A273911 (* Trim full grid to reflect growth by one cell at each stage *)
%t A273911 k=(Length[ca[[1]]]+1)/2;
%t A273911 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 A273911 Table[FromDigits[Part[ca[[i]][[i]],Range[i,2*i-1]],2], {i,1,stages-1}]
%Y A273911 Cf. A273910, A383609.
%K A273911 nonn,easy
%O A273911 0,2
%A A273911 _Robert Price_, Jun 03 2016