cp's OEIS Frontend

A282387 Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 462", based on the 5-celled von Neumann neighborhood.

%I A282387 #14 Feb 16 2025 08:33:41
%S A282387 1,3,6,15,24,60,102,255,384,960,1632,4080,6168,15420,26214,65535,
%T A282387 98304,245760,417792,1044480,1579008,3947520,6710784,16776960,
%U A282387 25166208,62915520,106956384,267390960,404232216,1010580540,1717986918,4294967295,6442450944
%N A282387 Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 462", based on the 5-celled von Neumann neighborhood.
%C A282387 Initialized with a single black (ON) cell at stage zero.
%C A282387 The first 23 terms of A062878 are the same as this sequence, but I cannot prove nor disprove that these two sequences are the same.
%C A282387 Agrees with A062878 for at least 1000 terms. - _Sean A. Irvine_, Apr 14 2023
%D A282387 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A282387 Robert Price, <a href="/A282387/b282387.txt">Table of n, a(n) for n = 0..126</a>
%H A282387 Robert Price, <a href="/A282387/a282387.tmp.txt">Diagrams of first 20 stages</a>
%H A282387 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 A282387 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A282387 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A282387 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>
%H A282387 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A282387 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A282387 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A282387 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}];
%t A282387 code = 462; stages = 128;
%t A282387 rule = IntegerDigits[code, 2, 10];
%t A282387 g = 2 * stages + 1; (* Maximum size of grid *)
%t A282387 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *)
%t A282387 ca = a;
%t A282387 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
%t A282387 PrependTo[ca, a];
%t A282387 (* Trim full grid to reflect growth by one cell at each stage *)
%t A282387 k = (Length[ca[[1]]] + 1)/2;
%t A282387 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 A282387 Table[FromDigits[Part[ca[[i]] [[i]], Range[1, i]], 2], {i, 1, stages - 1}]
%Y A282387 Cf. A062878. A282385, A282386, A282388.
%K A282387 nonn,easy
%O A282387 0,2
%A A282387 _Robert Price_, Feb 13 2017