%I
%S 1,1,7,15,7,63,63,255,511,1023,127,4095,255,16383,2047,65535,12799,
%T 262143,102399,1048575,1015807,4194303,8388607,16777215,16515071,
%U 67108863,33357823,268435455,7995391,1073741823,4194303,4294967295,16252927,17179869183
%N Decimal representation of the diagonal from the origin to the corner of the nth stage of growth of the twodimensional cellular automaton defined by "Rule 865", based on the 5celled 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="/A290621/b290621.txt">Table of n, a(n) for n = 0..126</a>
%H Robert Price, <a href="/A290621/a290621.tmp.txt">Diagrams of first 20 stages</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 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</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_5Neighbor_Cellular_Automata">Index to 2D 5Neighbor 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 = 865; 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 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i  1]], 10], {i, 1, stages  1}]
%Y Cf. A290618, A290619, A290620.
%K nonn,easy
%O 0,3
%A _Robert Price_, Aug 07 2017
