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%I #15 Apr 19 2019 11:44:55
%S 1,1,11010,111011,111011100,1011101111,1101101110000,11111110111111,
%T 11100000111000000,101111101011111111,110110001101100000000,
%U 1111111011111111111111,1110000011100000000000000,10111110101111111111111111,11011000110110000000000000000
%N Binary 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="/A267293/b267293.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)+100000000*a(n-4)-100000000*a(n-6) for n>12.
%F G.f.: (1 +x +11009*x^2 +111010*x^3 +11000090*x^4 +910990100*x^5 +90098900*x^6 +9099010000*x^7 -1109990110000*x^8 +979901000000*x^9 -108789011000000*x^10 -989900000000*x^11 +109898900000000*x^12) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 +10000*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]]],{k,1,rows}] (* Binary Representation of Rows *)
%Y Cf. A267292.
%K nonn,easy
%O 0,3
%A _Robert Price_, Jan 12 2016
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