login
Decimal representation of the middle column of the "Rule 169" elementary cellular automaton starting with a single ON (black) cell.
1

%I #15 Apr 20 2019 08:48:33

%S 1,2,5,10,20,41,83,167,335,671,1343,2687,5375,10751,21503,43007,86015,

%T 172031,344063,688127,1376255,2752511,5505023,11010047,22020095,

%U 44040191,88080383,176160767,352321535,704643071,1409286143,2818572287,5637144575,11274289151

%N Decimal representation of the middle column of the "Rule 169" 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="/A267589/b267589.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 18 2016 and Apr 20 2019: (Start)

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

%F G.f.: (1-x+x^2-x^3+x^5) / ((1-x)*(1-2*x)).

%F (End)

%t rule=169; 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],2],{k,1,rows}] (* Binary Representation of Middle Column *)

%Y Cf. A264442.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 18 2016