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A267884 Total number of OFF (white) cells after n iterations of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell. 1

%I

%S 0,3,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,

%T 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,

%U 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6

%N Total number of OFF (white) cells after n iterations of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

%H Robert Price, <a href="/A267884/b267884.txt">Table of n, a(n) for n = 0..1000</a>

%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_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F From _Colin Barker_, Jan 24 2016: (Start)

%F a(n) = 6 for n>2.

%F a(n) = a(n-1) for n>3.

%F G.f.: x*(3+2*x+x^2) / (1-x).

%F (End)

%t rule=233; rows=20; ca=CellularAutomaton[rule,{{1},0},rows-1,{All,All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]],{rows-k+1,rows+k-1}],{k,1,rows}]; (* Truncated list of each row *) nbc=Table[Total[catri[[k]]],{k,1,rows}]; (* Number of Black cells in stage n *) nwc=Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc,k]],{k,1,rows}] (* Number of White cells through stage n *)

%o (PARI) concat(0, Vec(x*(3+2*x+x^2)/(1-x) + O(x^100))) \\ _Colin Barker_, Jan 24 2016

%Y Cf. A267868.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 21 2016

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Last modified March 20 09:35 EDT 2019. Contains 321345 sequences. (Running on oeis4.)