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%I #17 May 06 2024 16:27:46
%S 1,3,5,11,21,43,85,171,341,683,1365,2987,5973,11435,24405,48555,97621,
%T 196267,392533,785323,1571413,3141547,6291029,12581803,25164629,
%U 50331307,100662613,201325483,402651733,805302187,1610612309,3221224363,6442449749,12884901547
%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 998", based on the 5-celled von Neumann neighborhood.
%C Initialized with a single black (ON) cell at stage zero.
%C Differs from A001045(n+2) from a(11) = 2987 on. - _M. F. Hasler_, Feb 13 2020
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H Robert Price, <a href="/A284547/b284547.txt">Table of n, a(n) for n = 0..126</a>
%H Robert Price, <a href="/A284547/a284547.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 06 2024: (Start)
%F a(n) = 2*a(n-1) + a(n-8) - 2*a(n-9) for n > 25.
%F G.f.: (1024*x^25 + 512*x^24 + 6400*x^22 - 768*x^21 + 768*x^20 + 1024*x^17 + 512*x^16 - 256*x^15 + 1536*x^14 - 512*x^13 + 256*x^11 - 2*x^8 + x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x + 1)/(2*x^9 - x^8 - 2*x + 1). (End)
%t CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t code = 998; 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. A284544, A284545, A284546.
%K nonn,easy
%O 0,2
%A _Robert Price_, Mar 28 2017
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