A266592 - OEIS

%I #18 Apr 18 2019 09:58:42

%S 1,11,111,1110,11101,111010,1110101,11101010,111010101,1110101010,

%T 11101010101,111010101010,1110101010101,11101010101010,

%U 111010101010101,1110101010101010,11101010101010101,111010101010101010,1110101010101010101,11101010101010101010

%N Binary representation of the middle column of the "Rule 37" 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="/A266592/b266592.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_, Jan 02 2016 and Apr 18 2019: (Start)

%F a(n) = (45*(-1)^n+1099*10^n-55)/990 for n>0.

%F a(n) = 10*a(n-1)+a(n-2)-10*a(n-3) for n>3.

%F G.f.: (1+x-x^3) / ((1-x)*(1+x)*(1-10*x)).

%F (End)

%t rule=37; 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 *) mc=Table[catri[[k]][[k]],{k,1,rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc,k]],{k,1,rows}]  (* Binary Representation of Middle Column *)

%Y Cf. A266588.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 01 2016