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A266662 Number of ON (black) cells in the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.

%I A266662 #20 Feb 16 2025 08:33:28
%S A266662 1,2,2,5,2,9,2,13,2,17,2,21,2,25,2,29,2,33,2,37,2,41,2,45,2,49,2,53,2,
%T A266662 57,2,61,2,65,2,69,2,73,2,77,2,81,2,85,2,89,2,93,2,97,2,101,2,105,2,
%U A266662 109,2,113,2,117,2,121,2,125,2,129,2,133,2,137,2,141
%N A266662 Number of ON (black) cells in the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.
%D A266662 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266662 Robert Price, <a href="/A266662/b266662.txt">Table of n, a(n) for n = 0..1000</a>
%H A266662 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266662 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A266662 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266662 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A266662 Conjectures from _Colin Barker_, Jan 03 2016 and Apr 18 2019: (Start)
%F A266662 a(n) = (-2*(-1)^n*n+2*n+3*(-1)^n+1)/2 for n>1.
%F A266662 a(n) = 2*a(n-2)-a(n-4) for n>5.
%F A266662 G.f.: (1+2*x+x^3-x^4+x^5) / ((1-x)^2*(1+x)^2).
%F A266662 (End)
%F A266662 a(n) = A266256(n), n>1. - _R. J. Mathar_, Jan 10 2016
%t A266662 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[Total[catri[[k]]],{k,1,rows}] (* Number of Black cells in stage n *)
%Y A266662 Cf. A266659.
%K A266662 nonn,easy
%O A266662 0,2
%A A266662 _Robert Price_, Jan 02 2016