cp's OEIS Frontend

A266721 Decimal representation of the middle column of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.

%I A266721 #32 Feb 16 2025 08:33:28
%S A266721 1,2,5,11,22,45,90,181,362,725,1450,2901,5802,11605,23210,46421,92842,
%T A266721 185685,371370,742741,1485482,2970965,5941930,11883861,23767722,
%U A266721 47535445,95070890,190141781,380283562,760567125,1521134250,3042268501,6084537002,12169074005
%N A266721 Decimal representation of the middle column of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
%H A266721 Robert Price, <a href="/A266721/b266721.txt">Table of n, a(n) for n = 0..1000</a>
%H A266721 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266721 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.
%H A266721 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266721 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A266721 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).
%F A266721 From _Colin Barker_, Jan 05 2016 and Apr 17 2019: (Start)
%F A266721 a(n) = (-2*(-1)^n+17*2^n-6)/12 for n>1.
%F A266721 a(n) = 2*a(n-1)+a(n-2)-2*a(n-3) for n>4.
%F A266721 G.f.: (1+x^3-x^4) / ((1-x)*(1+x)*(1-2*x)). (End)
%F A266721 a(n) = floor(17*2^n/12). - _Karl V. Keller, Jr._, Oct 17 2021
%t A266721 rule=59; 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 *)
%o A266721 (Python) print([17*2**n//12  for n in range(50)]) # _Karl V. Keller, Jr._, Oct 18 2021
%Y A266721 Cf. A266716, A266719, A266720.
%K A266721 nonn,easy
%O A266721 0,2
%A A266721 _Robert Price_, Jan 03 2016