A266327 - OEIS

%I #24 Jul 01 2023 15:10:37

%S 1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,

%T 11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,

%U 1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11,1,11

%N Binary representation of the n-th iteration of the "Rule 20" elementary cellular automaton starting with a single ON (black) cell.

%C Rules 52, 148 and 180 also generate this sequence.

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

%H Robert Price, <a href="/A266327/b266327.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_, Dec 28 2015 and Apr 18 2019: (Start)

%F a(n) = 6-5*(-1)^n.

%F a(n) = a(n-2) for n>1.

%F G.f.: (1+11*x) / ((1-x)*(1+x)).

%F (End)

%t rule=20; 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 *) Table[FromDigits[catri[[k]]],{k,1,rows}] (* Binary Representation of Rows *)

%Y Cf. A266326.

%K nonn,easy

%O 0,2

%A _Robert Price_, Dec 27 2015