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%I #13 Apr 14 2019 11:53:49
%S 1,2,4,9,11,20,22,35,37,54,56,77,79,104,106,135,137,170,172,209,211,
%T 252,254,299,301,350,352,405,407,464,466,527,529,594,596,665,667,740,
%U 742,819,821,902,904,989,991,1080,1082,1175,1177,1274,1276,1377,1379
%N Total number of ON (black) cells after n iterations 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="/A266257/b266257.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) = ((n+1)^2-(-1)^n*(n-1))/2.
%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>4.
%F G.f.: (1+x+3*x^3-x^4) / ((1-x)^3*(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 *) nbc=Table[Total[catri[[k]]],{k,1,rows}]; (* Number of Black cells in stage n *) Table[Total[Take[nbc,k]],{k,1,rows}] (* Number of Black cells through stage n *)
%Y Cf. A266253.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 25 2015
%E Conjectures from _Colin Barker_, Apr 14 2019
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