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A269709 Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 14", based on the 5-celled von Neumann neighborhood. 1

%I

%S 1,6,14,34,54,86,126,202,270,350,438,562,686,846,1030,1322,1582,1854,

%T 2134,2450,2766,3118,3494,3978,4438,4934,5454,6082,6710,7446,8254,

%U 9386,10414,11454,12502,13586,14670,15790,16934,18186,19414,20678,21966,23362

%N Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 14", based on the 5-celled von Neumann neighborhood.

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

%C Rules 46, 142 and 174 also generate this sequence.

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

%H Robert Price, <a href="/A269709/b269709.txt">Table of n, a(n) for n = 0..300</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=14; 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[Total[Part[on,Range[1,i]]],{i,1,Length[on]}] (* Sum at each stage *)

%Y Cf. A269707.

%K nonn,easy

%O 0,2

%A _Robert Price_, Mar 04 2016

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Last modified April 16 12:45 EDT 2021. Contains 343037 sequences. (Running on oeis4.)