%I #24 Aug 19 2021 21:28:32
%S 1,0,101,1100000,11101,11110100000,11101,111111110100000,11101,
%T 1111111111110100000,11101,11111111111111110100000,11101,
%U 111111111111111111110100000,11101,1111111111111111111111110100000,11101,11111111111111111111111111110100000,11101
%N Binary representation of the n-th iteration of the "Rule 9" 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="/A266244/b266244.txt">Table of n, a(n) for n = 0..999</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 From _Colin Barker_, Dec 28 2015 and Apr 14 2019: (Start)
%F a(n) = 10001*a(n-2) - 10000*a(n-4) for n>7.
%F G.f.: (1 -9900*x^2 +1100000*x^3 -989000*x^4 +109000000*x^5 -110000000*x^6 +10000000000*x^7) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)).
%F (End)
%F a(n) = floor(100^n/10) + floor(1011010*100^n/999900) - 1011010 for odd n>3; a(n) = 11101 for even n>3. - _Karl V. Keller, Jr._, Aug 19 2021
%t rule=9; 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 *)
%o (Python) print([1, 0, 101, 1100000]+[100**n//10 + 1011010*100**n//999900 - 1011010 if n%2 else 11101 for n in range(4,30)]) # _Karl V. Keller, Jr._, Aug 19 2021
%Y Cf. A266243, A266245.
%K nonn,easy
%O 0,3
%A _Robert Price_, Dec 25 2015