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%I #15 Jul 28 2018 10:45:05
%S 1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,1,
%T 1,1,1,1,1,1,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1,1,1,1,
%U 1,1,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1
%N Triangle read by rows giving successive states of cellular automaton generated by "Rule 201" initiated with a single ON (black) cell.
%C Row n has length 2n+1.
%C The fact that only n cells to the left and right of the initially active cell are updated at step n is contradictory to the usual treatment of a "Rule m" automaton, where all cells are updated depending on their neighborhood. See also the illustration of "Rule 201" on the MathWorld page. - _M. F. Hasler_, Jul 28 2018
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H Robert Price, <a href="/A267679/b267679.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 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>
%e The first ten rows:
%e 1
%e 0 0 0
%e 1 0 1 0 1
%e 1 1 0 0 0 1 1
%e 1 1 1 0 1 0 1 1 1
%e 1 1 1 1 0 0 0 1 1 1 1
%e 1 1 1 1 1 0 1 0 1 1 1 1 1
%e 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1
%e 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1
%e 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1
%t rule=201; 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 *)
%o (PARI) A267679_row(n)=if(n==1,[0,0,0],binary(1<<(n*2+1)-(bittest(n,0)*2+5)<<(n-1)-1)) \\ _M. F. Hasler_, Jul 28 2018
%Y Cf. A267681 (value of row n read as binary number). - _M. F. Hasler_, Jul 28 2018
%K nonn,tabf,easy
%O 0
%A _Robert Price_, Jan 19 2016
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