A266846 - OEIS

%I #20 Jun 13 2022 21:37:29

%S 1,6,20,104,336,1696,5440,27264,87296,436736,1397760,6989824,22368256,

%T 111845376,357908480,1789558784,5726601216,28633071616,91625881600,

%U 458129670144,1466015154176,7330076819456,23456246661120,117281237499904,375299963355136

%N Decimal representation of the n-th iteration of the "Rule 70" 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="/A266846/b266846.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 05 2016 and Apr 18 2019: (Start)

%F a(n) = 2^(n-1)*(-(-2)^n+9*2^n-2)/3 = 2^(n-1)*A061547(n+3).

%F a(n) = 2*a(n-1)+16*a(n-2)-32*a(n-3) for n>2.

%F G.f.: (1+4*x-8*x^2) / ((1-2*x)*(1-4*x)*(1+4*x)).

%F (End)

%t rule=70; 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[FromDigits[catri[[k]],2],{k,1,rows}]   (* Decimal Representation of Rows *)

%Y Cf. A266843, A266844.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 04 2016