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%I #23 Apr 19 2019 05:28:39
%S 0,1,2,1,6,1,10,1,14,1,18,1,22,1,26,1,30,1,34,1,38,1,42,1,46,1,50,1,
%T 54,1,58,1,62,1,66,1,70,1,74,1,78,1,82,1,86,1,90,1,94,1,98,1,102,1,
%U 106,1,110,1,114,1,118,1,122,1,126,1,130,1,134,1,138,1
%N Number of OFF (white) cells in the n-th iteration of the "Rule 123" 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="/A267354/b267354.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 14 2016: (Start)
%F a(n) = ((2*(-1)^n+2)*n-3*(-1)^n-1)/2 for n>0.
%F a(n) = 2*a(n-2)-a(n-4) for n>4.
%F G.f.: x*(1+2*x-x^2+2*x^3) / ((1-x)^2*(1+x)^2).
%F (End)
%F a(n) = A266303(n-1). - _R. J. Mathar_, Jan 17 2016
%t rule=123; 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. A267349.
%K nonn
%O 0,3
%A _Robert Price_, Jan 13 2016
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