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%I #32 Dec 15 2021 21:39:58
%S 1,10,101,1010,10101,101011,1010110,10101101,101011010,1010110101,
%T 10101101010,101011010101,1010110101010,10101101010101,
%U 101011010101010,1010110101010101,10101101010101010,101011010101010101,1010110101010101010,10101101010101010101
%N Binary representation of the middle column of the "Rule 9" elementary cellular automaton starting with a single ON (black) cell.
%D Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H Robert Price, <a href="/A266247/b266247.txt">Table of n, a(n) for n = 0..999</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</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_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,1,-10).
%F From _Colin Barker_, Dec 28 2015 and Apr 14 2019: (Start)
%F a(n) = (-45000*(-1)^n + 1000009*10^n - 55000)/990000 for n > 3.
%F a(n) = 10*a(n-1) + a(n-2) - 10*a(n-3) for n > 6.
%F G.f.: (1 + x^5 - x^6) / ((1-x)*(1+x)*(1-10*x)).
%F (End)
%F a(n) = floor((100000*10^n/9 + 100001*10^n)/110000). - _Karl V. Keller, Jr._, Dec 15 2021
%t rule=9; 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]],{k,1,rows}] (* Binary Representation of Middle Column *)
%o (Python) print([(100000*10**n//9 + 100001*10**n)//110000 for n in range(50)]) # _Karl V. Keller, Jr._, Dec 15 2021
%Y Cf. A266243, A266248.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 25 2015
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