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Number of OFF (white) cells in the n-th iteration of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell.
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%I #14 Apr 20 2019 08:46:37

%S 0,2,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,

%T 16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,

%U 28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36

%N Number of OFF (white) cells in the n-th iteration of the "Rule 141" 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="/A267530/b267530.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 17 2016 and Apr 20 2019: (Start)

%F a(n) = a(n-1)+a(n-2)-a(n-3) for n>4.

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

%F (End)

%t rule=141; 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. A267525.

%Y Essentially the same as A008619.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 16 2016