A267366 - OEIS

%I #19 Jan 24 2023 05:35:03

%S 1,11,110,1101,11010,110100,1101000,11010001,110100010,1101000100,

%T 11010001000,110100010000,1101000100000,11010001000000,

%U 110100010000000,1101000100000001,11010001000000010,110100010000000100,1101000100000001000,11010001000000010000

%N Binary representation of the middle column of the "Rule 126" elementary cellular automaton starting with a single ON (black) cell.

%C The middle column itself is A036987. [Noticed by _Dominik Koeppl_, Oct 21 2022]

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

%H Robert Price, <a href="/A267366/b267366.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="/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%t rule=126; 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. A267367 (decimal), A071035, A036987, A209229.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 13 2016