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%I #14 Apr 14 2019 11:53:16
%S 0,3,6,11,16,22,31,37,50,56,73,79,100,106,131,137,166,172,205,211,248,
%T 254,295,301,346,352,401,407,460,466,523,529,590,596,661,667,736,742,
%U 815,821,898,904,985,991,1076,1082,1171,1177,1270,1276,1373,1379,1480
%N Total number of OFF (white) cells after n iterations of the "Rule 9" 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="/A266252/b266252.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 28 2015 and Apr 14 2019: (Start)
%F a(n) = ((-1)^n*(n-4)+n*(n+4))/2 for n>2.
%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>7.
%F G.f.: x*(3+3*x-x^2-x^3-x^4+2*x^5-x^6) / ((1-x)^3*(1+x)^2).
%F (End)
%t rule=9; 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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc,k]],{k,1,rows}] (* Number of White cells through stage n *)
%Y Cf. A266243.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 25 2015
%E Conjectures from _Colin Barker_, Apr 14 2019
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