%I #14 Apr 19 2019 11:10:10
%S 1,3,6,11,16,23,29,40,46,61,67,86,92,115,121,148,154,185,191,226,232,
%T 271,277,320,326,373,379,430,436,491,497,556,562,625,631,698,704,775,
%U 781,856,862,941,947,1030,1036,1123,1129,1220,1226,1321,1327,1426,1432
%N Total number of ON (black) cells after n iterations of the "Rule 111" 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="/A267260/b267260.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 13 2016 and Apr 19 2019: (Start)
%F a(n) = (n^2-((-1)^n-4)*n+4*(-1)^n)/2 for n>3.
%F G.f.: (1+2*x+x^2+x^3-x^5-x^6+2*x^7-x^8) / ((1-x)^3*(1+x)^2).
%F (End)
%t rule=111; 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. A267253.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 12 2016
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