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%I #16 Apr 20 2019 05:56:30
%S 1,1,4,10,19,30,43,58,75,94,115,138,163,190,219,250,283,318,355,394,
%T 435,478,523,570,619,670,723,778,835,894,955,1018,1083,1150,1219,1290,
%U 1363,1438,1515,1594,1675,1758,1843,1930,2019,2110,2203,2298,2395,2494
%N Total number of ON (black) cells after n iterations of the "Rule 233" 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="/A267882/b267882.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 22 2016 and Apr 20 2019: (Start)
%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>2.
%F G.f.: (1-2*x+4*x^2-x^5) / (1-x)^3.
%F (End)
%t rule=233; 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. A267868.
%K nonn,easy
%O 0,3
%A _Robert Price_, Jan 21 2016