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%I #12 May 05 2024 17:06:58
%S 1,3,3,15,3,7,43,255,131,775,683,4095,2307,12935,10027,51839,40067,
%T 211207,160427,845823,641283,3379847,2565931,13519487,10263683,
%U 54081799,41054891,216328191,164219139,865309319,656877355,3461237375,2627509379,13844953351
%N 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 446", based on the 5-celled 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="/A282264/b282264.txt">Table of n, a(n) for n = 0..126</a>
%H Robert Price, <a href="/A282264/a282264.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_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F Conjectures from _Chai Wah Wu_, May 05 2024: (Start)
%F a(n) = 4*a(n-2) + a(n-8) - 4*a(n-10) for n > 17.
%F G.f.: (4096*x^17 - 128*x^15 + 768*x^14 - 3392*x^13 - 416*x^12 + 992*x^11 + 160*x^10 - 248*x^9 - 42*x^8 + 227*x^7 + 31*x^6 - 53*x^5 - 9*x^4 + 3*x^3 - x^2 + 3*x + 1)/(4*x^10 - x^8 - 4*x^2 + 1). (End)
%t CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t code = 446; 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]], 2], {i ,1, stages - 1}]
%Y Cf. A282261, A282262, A282263.
%K nonn,easy
%O 0,2
%A _Robert Price_, Feb 10 2017
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