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

Search: id:a283702
Showing 1-1 of 1

%I A283702 #7 Mar 17 2017 00:45:20
%S A283702 1,3,5,11,21,43,69,219,261,795,1365,2731,4373,14187,16389,49179,81989,
%T A283702 180699,345365,711531,1115221,3612075,4280389,13021659,22107397,
%U A283702 45525787,67392853,203270827,340853013,766969707,1342246917,2953277467,5638213701,11550175707
%N A283702 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 710", based on the 5-celled von Neumann neighborhood.
%C A283702 Initialized with a single black (ON) cell at stage zero.
%D A283702 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A283702 Robert Price, <a href="/A283702/b283702.txt">Table of n, a(n) for n = 0..126</a>
%H A283702 Robert Price, <a href="/A283702/a283702.tmp.txt">Diagrams of first 20 stages</a>
%H A283702 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 A283702 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A283702 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A283702 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A283702 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A283702 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A283702 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A283702 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A283702 code = 710; stages = 128;
%t A283702 rule = IntegerDigits[code, 2, 10];
%t A283702 g = 2 * stages + 1; (* Maximum size of grid *)
%t A283702 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A283702 ca = a;
%t A283702 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A283702 PrependTo[ca, a];
%t A283702 (* Trim full grid to reflect growth by one cell at each stage *)
%t A283702 k = (Length[ca[[1]]] + 1)/2;
%t A283702 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 A283702 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 2], {i ,1, stages - 1}]
%Y A283702 Cf. A283699, A283700, A283701.
%K A283702 nonn,easy
%O A283702 0,2
%A A283702 _Robert Price_, Mar 14 2017

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