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Decimal representation of the middle column of the "Rule 147" elementary cellular automaton starting with a single ON (black) cell.
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%I #24 May 14 2021 17:31:20

%S 1,2,4,9,19,38,76,153,307,614,1228,2457,4915,9830,19660,39321,78643,

%T 157286,314572,629145,1258291,2516582,5033164,10066329,20132659,

%U 40265318,80530636,161061273,322122547,644245094,1288490188,2576980377,5153960755,10307921510

%N Decimal representation of the middle column of the "Rule 147" 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="/A262864/b262864.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>

%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>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,3,-2).

%F From _Colin Barker_, Jan 17 2016 and Apr 16 2019: (Start)

%F a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3) - 2*a(n-4) for n > 3.

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

%F (End)

%F a(n) = floor(6*2^n/5). - _Karl V. Keller, Jr._, Apr 12 2021

%t rule=147; 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 (Python) print([6*2**n//5 for n in range(50)]) # _Karl V. Keller, Jr._, Apr 12 2021

%Y Cf. A262808, A262863 (in binary).

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 17 2016