A267524 - OEIS

%I #26 Oct 30 2024 19:34:47

%S 1,10,100,1001,10011,100111,1001111,10011111,100111111,1001111111,

%T 10011111111,100111111111,1001111111111,10011111111111,

%U 100111111111111,1001111111111111,10011111111111111,100111111111111111,1001111111111111111,10011111111111111111

%N Binary representation of the middle column of the "Rule 139" 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="/A267524/b267524.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 16 2016 and Apr 19 2019: (Start)

%F a(n) = 11*a(n-1) - 10*a(n-2) for n > 3. [n range correction - _Karl V. Keller, Jr._, Apr 08 2022]

%F G.f.: (1-x+x^3) / ((1-x)*(1-10*x)).

%F (End)

%t rule=139; 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. A267520, A054135.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 16 2016