%I #14 Jul 28 2024 11:00:18

%S 4,7,4,20,-12,36,-16,72,-72,84,-8,80,-56,116,-16,52,-28,100,24,-4,-4,

%T 108,100,-28,-60,252,36,-36,-44,180,168,-224,40,276,148,-76,-132,220,

%U 376,-292,-84,472,192,-300,-32,340,344,-240,-236,524,440,-472,-268,756

%N First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 30", 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="/A269756/b269756.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=30; 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. A269753.

%K sign,easy

%O 0,1

%A _Robert Price_, Mar 04 2016