A266444 - OEIS

%I #21 Apr 16 2019 06:26:46

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

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

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

%N Middle column of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.

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

%H Robert Price, <a href="/A266444/b266444.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 31 2015 and Apr 16 2019: (Start)

%F a(n) = (1-(-1)^n)/2 for n>11.

%F a(n) = a(n-2) for n>13.

%F G.f.: (1-x^2+x^4+x^9-x^10-x^11+x^13) / ((1-x)*(1+x)).

%F (End)

%t rule=25; 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[catri[[k]][[k]],{k,1,rows}] (* Keep only middle cell from each row *)

%Y Cf. A266441.

%K nonn,easy

%O 0

%A _Robert Price_, Dec 29 2015