cp's OEIS Frontend

A269698 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 6", based on the 5-celled von Neumann neighborhood.

%I A269698 #18 Feb 16 2025 08:33:30
%S A269698 4,-1,16,-16,16,-4,64,-76,16,-4,64,-64,64,-16,256,-316,16,-4,64,-64,
%T A269698 64,-16,256,-304,64,-16,256,-256,256,-64,1024,-1276,16,-4,64,-64,64,
%U A269698 -16,256,-304,64,-16,256,-256,256,-64,1024,-1264,64,-16,256,-256,256,-64
%N A269698 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 6", based on the 5-celled von Neumann neighborhood.
%C A269698 Initialized with a single black (ON) cell at stage zero.
%C A269698 Rules 38, 70, 102, 134, 166, 198 and 230 also generate this sequence.
%D A269698 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A269698 Robert Price, <a href="/A269698/b269698.txt">Table of n, a(n) for n = 0..299</a>
%H A269698 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 A269698 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A269698 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A269698 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A269698 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A269698 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A269698 rule=6; stages=300;
%t A269698 ca=CellularAutomaton[{rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}},{{{1}},0},stages]; (* Start with single black cell *)
%t A269698 on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%t A269698 Table[on[[i+1]]-on[[i]],{i,1,Length[on]-1}] (* Difference at each stage *)
%Y A269698 Cf. A269695.
%K A269698 sign,easy
%O A269698 0,1
%A A269698 _Robert Price_, Mar 03 2016