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%I #17 Apr 19 2019 11:44:59
%S 1,1,26,59,476,751,7024,16319,115136,195327,1776384,4177919,29474816,
%T 50003967,454754304,1069547519,7545552896,12801015807,116417101824,
%U 273804165119,1931661541376,3277060046847,29802778066944,70093866270719,494505354592256
%N Decimal representation of the n-th iteration of the "Rule 121" 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="/A267294/b267294.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 15 2016 and Apr 19 2019: (Start)
%F a(n) = a(n-2)+256*a(n-4)-256*a(n-6) for n>12.
%F G.f.: (1 +x +25*x^2 +58*x^3 +194*x^4 +436*x^5 +148*x^6 +720*x^7 -7088*x^8 +1856*x^9 -15040*x^10 -2816*x^11 +21760*x^12) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1+16*x^2)).
%F (End)
%t rule=121; 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 *) Table[FromDigits[catri[[k]],2],{k,1,rows}] (* Decimal Representation of Rows *)
%Y Cf. A267292.
%K nonn,easy
%O 0,3
%A _Robert Price_, Jan 12 2016
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