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%I #20 Apr 18 2019 11:41:42
%S 0,1,4,6,13,15,26,28,43,45,64,66,89,91,118,120,151,153,188,190,229,
%T 231,274,276,323,325,376,378,433,435,494,496,559,561,628,630,701,703,
%U 778,780,859,861,944,946,1033,1035,1126,1128,1223,1225,1324,1326,1429
%N Total number of OFF (white) cells after n iterations of the "Rule 47" 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="/A266665/b266665.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 03 2016 and Apr 18 2019: (Start)
%F a(n) = (n^2+2*n+(-1)^n*(n-1)-1)/2 for n>0.
%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>5.
%F G.f.: x*(1+3*x+x^3-x^4) / ((1-x)^3*(1+x)^2).
%F (End)
%t rule=47; 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. A266659.
%K nonn,easy
%O 0,3
%A _Robert Price_, Jan 02 2016
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