A269698 - OEIS

%I #17 Jul 28 2024 10:59:54

%S 4,-1,16,-16,16,-4,64,-76,16,-4,64,-64,64,-16,256,-316,16,-4,64,-64,

%T 64,-16,256,-304,64,-16,256,-256,256,-64,1024,-1276,16,-4,64,-64,64,

%U -16,256,-304,64,-16,256,-256,256,-64,1024,-1264,64,-16,256,-256,256,-64

%N 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 Initialized with a single black (ON) cell at stage zero.

%C Rules 38, 70, 102, 134, 166, 198 and 230 also generate this sequence.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

%H Robert Price, <a href="/A269698/b269698.txt">Table of n, a(n) for n = 0..299</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 <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>

%t rule=6; stages=300;

%t ca=CellularAutomaton[{rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}},{{{1}},0},stages]; (* Start with single black cell *)

%t on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)

%t Table[on[[i+1]]-on[[i]],{i,1,Length[on]-1}] (* Difference at each stage *)

%Y Cf. A269695.

%K sign,easy

%O 0,1

%A _Robert Price_, Mar 03 2016