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%I #36 Jul 06 2023 13:02:06
%S 1,11,111,1110,11101,111010,1110101,11101010,111010100,1110101001,
%T 11101010011,111010100111,1110101001110,11101010011101,
%U 111010100111010,1110101001110101,11101010011101010,111010100111010101,1110101001110101010,11101010011101010101
%N Binary representation of the middle column of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
%H Robert Price, <a href="/A266790/b266790.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 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>
%F Conjectures from _Colin Barker_, Jan 04 2016 and Apr 18 2019: (Start)
%F a(n) = (-9*(-1)^n+1098999991099*2^(n-9)*5^(n-10)-11)/198 for n>9.
%F G.f.: (1+x-x^3-x^8+x^9+x^10-x^12) / ((1-x)*(1+x)*(1-10*x)).
%F (End)
%t rule=61; 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 *) mc=Table[catri[[k]][[k]],{k,1,rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc,k]],{k,1,rows}] (* Binary Representation of Middle Column *)
%Y Cf. A266786, A266789, A266791.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 03 2016