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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.

%I A267884 #22 Jun 24 2025 12:30:54
%S A267884 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 A267884 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 A267884 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6
%N A267884 Total number of OFF (white) cells after n iterations of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.
%D A267884 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A267884 Robert Price, <a href="/A267884/b267884.txt">Table of n, a(n) for n = 0..1000</a>
%H A267884 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267884 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A267884 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267884 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A267884 Conjectures from _Colin Barker_, Jan 24 2016 and Apr 20 2019: (Start)
%F A267884 a(n) = 6 for n>2.
%F A267884 a(n) = a(n-1) for n>3.
%F A267884 G.f.: x*(3+2*x+x^2) / (1-x).
%F A267884 (End)
%t A267884 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 *)
%Y A267884 Cf. A101101, A267868.
%K A267884 nonn,easy
%O A267884 0,2
%A A267884 _Robert Price_, Jan 21 2016