%I #14 Oct 14 2021 03:30:22
%S 1,0,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,1,1,1,1,1,1,
%T 1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,
%U 1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0
%N Triangle read by rows giving successive states of cellular automaton generated by "Rule 53" initiated with a single ON (black) cell.
%C Row n has length 2n+1.
%H Robert Price, <a href="/A266669/b266669.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.
%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>
%e The first ten rows:
%e 1
%e 0 1 1
%e 0 1 0 0 0
%e 1 0 1 1 1 1 1
%e 0 0 1 0 0 0 0 0 0
%e 1 1 0 1 1 1 1 1 1 1 1
%e 0 0 0 1 0 0 0 0 0 0 0 0 0
%e 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1
%e 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
%e 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
%t rule=53; 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 *) Flatten[catri] (* Triangle Representation of CA *)
%Y Cf. A266670, A266671, A266605 (rows reversed).
%K nonn,tabf,easy
%O 0
%A _Robert Price_, Jan 02 2016