login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Binary representation of the middle column of the "Rule 126" elementary cellular automaton starting with a single ON (black) cell.
2

%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