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%I #21 Dec 01 2020 07:44:39
%S 0,2,4,6,6,8,8,10,10,12,12,14,14,16,16,18,18,20,20,22,22,24,24,26,26,
%T 28,28,30,30,32,32,34,34,36,36,38,38,40,40,42,42,44,44,46,46,48,48,50,
%U 50,52,52,54,54,56,56,58,58,60,60,62,62,64,64,66,66,68
%N Number of OFF (white) cells in the n-th iteration of the "Rule 133" 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="/A267460/b267460.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>
%F Conjectures from _Colin Barker_, Jan 16 2016: (Start)
%F a(n) = (2*n-(-1)^n+5)/2 for n>1.
%F a(n) = a(n-1)+a(n-2)-a(n-3) for n>4.
%F G.f.: 2*x*(1+x-x^3) / ((1-x)^2*(1+x)).
%F (End)
%t rule=133; 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 *) Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}] (* Number of White cells in stage n *)
%Y Cf. A267423.
%Y Cf. A052928, A265283, A213222.
%K nonn
%O 0,2
%A _Robert Price_, Jan 15 2016
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