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A267367 Decimal representation of the middle column of the "Rule 126" elementary cellular automaton starting with a single ON (black) cell.

%I A267367 #22 Feb 16 2025 08:33:29
%S A267367 1,3,6,13,26,52,104,209,418,836,1672,3344,6688,13376,26752,53505,
%T A267367 107010,214020,428040,856080,1712160,3424320,6848640,13697280,
%U A267367 27394560,54789120,109578240,219156480,438312960,876625920,1753251840,3506503681,7013007362
%N A267367 Decimal representation of the middle column of the "Rule 126" elementary cellular automaton starting with a single ON (black) cell.
%D A267367 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A267367 Robert Price, <a href="/A267367/b267367.txt">Table of n, a(n) for n = 0..1000</a>
%H A267367 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267367 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule126.html">Rule 126</a>
%H A267367 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A267367 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267367 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%p A267367 A267367 := proc(n) local i, s, z; s := 0; i := n; z := 1;
%p A267367 while 0 <= i do s := s+2^i; i := i-z; z := z+z od; s end:
%p A267367 seq(A267367(n), n=0..32); # _Peter Luschny_, Dec 02 2017
%t A267367 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],2],{k,1,rows}]  (* Binary Representation of Middle Column *)
%o A267367 (Python)
%o A267367 def A267367(n):
%o A267367     i, s, z = n, 0, 1
%o A267367     while 0 <= i: s += 1<<i; i -= z; z += z
%o A267367     return s
%o A267367 print([A267367(n) for n in range(33)]) # _Peter Luschny_, Dec 02 2017
%Y A267367 Cf. A267366 (binary), A001855, A071035, A267365.
%K A267367 nonn,easy
%O A267367 0,2
%A A267367 _Robert Price_, Jan 13 2016