A267533 - OEIS

%I #18 Apr 25 2022 08:09:03

%S 1,1,1,0,1,1,0,0,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,1,1,1,1,0,0,1,1,1,1,1,

%T 1,1,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1

%N Triangle read by rows giving successive states of cellular automaton generated by "Rule 143" initiated with a single ON (black) cell.

%C Row n has length 2n + 1.

%H Robert Price, <a href="/A267533/b267533.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>. See page 55.

%H Wolfram Research, <a href="http://atlas.wolfram.com/01/01/143/">Wolfram Atlas of Simple Programs: Rule 143</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                 1 1 0

%e               1 1 0 0 1

%e             1 1 0 0 1 1 1

%e           1 1 0 0 1 1 1 1 1

%e         1 1 0 0 1 1 1 1 1 1 1

%e       1 1 0 0 1 1 1 1 1 1 1 1 1

%e     1 1 0 0 1 1 1 1 1 1 1 1 1 1 1

%e   1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1

%e 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

%t rule = 143; 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, rows}]; (* Truncated list of each row *) Flatten[catri] (* Triangle Representation of CA *)

%Y Cf. A267535, A267536.

%Y Cf. A267537 (central column), A267800 (row reversals).

%K nonn,tabf,easy

%O 0

%A _Robert Price_, Jan 16 2016