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%I #23 Aug 28 2021 03:20:54
%S 1,100,11,1111100,11,11111111100,11,111111111111100,11,
%T 1111111111111111100,11,11111111111111111111100,11,
%U 111111111111111111111111100,11,1111111111111111111111111111100,11,11111111111111111111111111111111100,11
%N Binary representation of the n-th iteration of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.
%C Rule 43 also generates this sequence.
%H Robert Price, <a href="/A266254/b266254.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 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.
%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>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,10001,0,-10000).
%F From _Colin Barker_, Dec 26 2015 and Apr 14 2019: (Start)
%F a(n) = (199*(-1)^n+10^(2*n+1)-(-1)^n*10^(2*n+1)-1)/18 for n>0.
%F a(n) = 10001*a(n-2) - 10000*a(n-4) for n>4.
%F G.f.: (1+100*x-9990*x^2+111000*x^3-100000*x^4) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).
%F (End)
%F a(n) = (10*100^n - 100)/9 for odd n; a(n) = 11 - 10*0^n for even n. - _Karl V. Keller, Jr._, Aug 26 2021
%t rule=11; 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([(10*100**n - 100)//9 if n%2 else 11 - 10*0**n for n in range(50)]) # _Karl V. Keller, Jr._, Aug 26 2021
%Y Cf. A266253, A266255.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 25 2015
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