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%I #14 Apr 19 2019 07:10:40
%S 1,2,5,10,16,24,31,44,50,65,73,94,100,123,131,160,166,197,205,242,248,
%T 287,295,340,346,393,401,454,460,515,523,584,590,653,661,730,736,807,
%U 815,892,898,977,985,1070,1076,1163,1171,1264,1270,1365,1373,1474,1480
%N Total number of ON (black) cells after n iterations of the "Rule 107" 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="/A267159/b267159.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 11 2016 and Apr 19 2019: (Start)
%F a(n) = a(n-1)+a(n-2)-a(n-3)+a(n-4)-a(n-5)-a(n-6)+a(n-7) for n>12.
%F G.f.: (1+x+2*x^2+4*x^3+2*x^4+2*x^5-x^6+x^7-4*x^8-x^9+x^10+x^11-x^12) / ((1-x)^3*(1+x)^2*(1+x^2)).
%F (End)
%t rule=107; 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. A267152.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 11 2016
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