A266660 - OEIS

%I #34 Jul 06 2023 12:51:10

%S 1,110,11,1111100,11,11111111100,11,111111111111100,11,

%T 1111111111111111100,11,11111111111111111111100,11,

%U 111111111111111111111111100,11,1111111111111111111111111111100,11,11111111111111111111111111111111100,11

%N Binary representation of the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.

%H Robert Price, <a href="/A266660/b266660.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 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.

%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 03 2016 and Apr 18 2019: (Start)

%F a(n) = (199*(-1)^n+10^(2*n+1)-(-1)^n*10^(2*n+1)-1)/18 for n>1.

%F a(n) = 10001*a(n-2)-10000*a(n-4) for n>5.

%F G.f.: (1+110*x-9990*x^2+10990*x^3-100000*x^4+100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

%F (End)

%F a(n) = A266254(n), n>1. - _R. J. Mathar_, Jan 10 2016

%F Conjecture: a(n) = (10*100^n - 100)/9 for odd n > 1; a(n) = 11 for even n > 1. - _Karl V. Keller, Jr._, Oct 10 2021

%t rule=47; 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]]],{k,1,rows}] (* Binary Representation of Rows *)

%Y Cf. A266254, A266659, A266661.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 02 2016