A266982 - OEIS

%I #17 Mar 23 2016 09:12:45

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

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

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

%N Triangle read by rows giving successive states of cellular automaton generated by "Rule 81" initiated with a single ON (black) cell.

%C Row n has length 2n+1.

%C This sequence is also generated by rule 113.

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

%H Robert Price, <a href="/A266982/b266982.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>

%F Conjecture: a(0)=1; for n>0, a(n) = ( Sum_{i=1..n-2} floor((n-2)/i) ) mod 2. - _Wesley Ivan Hurt_, Mar 22 2016

%e The first ten rows:

%e                   1

%e                 0 0 1

%e               1 1 0 0 0

%e             0 0 1 1 1 1 1

%e           1 1 0 0 0 0 0 0 0

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

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

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

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

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

%t rule=81; 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 *)

%K nonn,tabf,easy

%O 0

%A _Robert Price_, Jan 07 2016