A267604 - OEIS

%I #57 Apr 24 2024 10:10:45

%S 1,3,6,13,27,55,111,223,447,895,1791,3583,7167,14335,28671,57343,

%T 114687,229375,458751,917503,1835007,3670015,7340031,14680063,

%U 29360127,58720255,117440511,234881023,469762047,939524095,1879048191,3758096383,7516192767

%N Decimal representation of the middle column of the "Rule 175" 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="/A267604/b267604.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^2+x^3) / ((1-x)*(1-2*x)). (End)

%F Conjectures from _Altug Alkan_, Jan 18 2016: (Start)

%F a(n) = A086224(n-2), for n > 1.

%F a(n) = ceiling((7/4)*2^n - 1). (End)

%t rule=175; 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. A086224, A265186, A266678, A266680.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 18 2016