A266664 - OEIS

%I #20 Apr 18 2019 11:03:47

%S 0,1,3,2,7,2,11,2,15,2,19,2,23,2,27,2,31,2,35,2,39,2,43,2,47,2,51,2,

%T 55,2,59,2,63,2,67,2,71,2,75,2,79,2,83,2,87,2,91,2,95,2,99,2,103,2,

%U 107,2,111,2,115,2,119,2,123,2,127,2,131,2,135,2,139,2

%N Number of OFF (white) cells in the n-th iteration of the "Rule 47" 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="/A266664/b266664.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 03 2016 and Apr 18 2019: (Start)

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

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

%F G.f.: x*(1+3*x+x^3-x^4) / ((1-x)^2*(1+x)^2).

%F (End)

%F a(n) = A266258(n), n>1. - _R. J. Mathar_, Jan 10 2016

%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 *) nbc=Table[Total[catri[[k]]],{k,1,rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}] (* Number of White cells in stage n *)

%Y Cf. A266659.

%K nonn,easy

%O 0,3

%A _Robert Price_, Jan 02 2016