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A266219 Binary representation of the middle column of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.

%I A266219 #32 Feb 16 2025 08:33:28
%S A266219 1,11,110,1101,11010,110101,1101010,11010101,110101010,1101010101,
%T A266219 11010101010,110101010101,1101010101010,11010101010101,
%U A266219 110101010101010,1101010101010101,11010101010101010,110101010101010101,1101010101010101010,11010101010101010101
%N A266219 Binary representation of the middle column of the "Rule 7" elementary cellular automaton starting with a single ON (black) cell.
%D A266219 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266219 Robert Price, <a href="/A266219/b266219.txt">Table of n, a(n) for n = 0..499</a>
%H A266219 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266219 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266219 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A266219 Conjectures from _Colin Barker_, Dec 25 2015 and Apr 13 2019: (Start)
%F A266219 a(n) = 1/198*(-9*(-1)^n+109*2^(n+1)*5^n-11).
%F A266219 a(n) = 10*a(n-1) + a(n-2) - 10*a(n-3) for n>2.
%F A266219 G.f.: (1+x-x^2) / ((1-x)*(1+x)*(1-10*x)).
%F A266219 (End)
%F A266219 Conjecture: a(n) = floor(109*10^n/99). - _Karl V. Keller, Jr._, Mar 16 2022
%t A266219 rule=7; 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 A266219 Cf. A266216, A081254.
%K A266219 nonn,easy
%O A266219 0,2
%A A266219 _Robert Price_, Dec 24 2015