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%I #14 Apr 14 2019 11:53:40
%S 1,1,2,5,2,9,2,13,2,17,2,21,2,25,2,29,2,33,2,37,2,41,2,45,2,49,2,53,2,
%T 57,2,61,2,65,2,69,2,73,2,77,2,81,2,85,2,89,2,93,2,97,2,101,2,105,2,
%U 109,2,113,2,117,2,121,2,125,2,129,2,133,2,137,2,141
%N Number of ON (black) cells in the n-th iteration of the "Rule 11" 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="/A266256/b266256.txt">Table of n, a(n) for n = 0..999</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</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_, Dec 27 2015 and Apr 14 2019: (Start)
%F a(n) = (-2*((-1)^n-1)*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.: (1+x+3*x^3-x^4) / ((1-x)^2*(1+x)^2).
%F (End)
%t rule=11; 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 *) Table[Total[catri[[k]]],{k,1,rows}] (* Number of Black cells in stage n *)
%Y Cf. A266253.
%K nonn,easy
%O 0,3
%A _Robert Price_, Dec 25 2015
%E Conjectures from _Colin Barker_, Apr 14 2019
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