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%I #28 Dec 15 2021 20:18:44
%S 1,2,5,10,21,43,86,173,346,693,1386,2773,5546,11093,22186,44373,88746,
%T 177493,354986,709973,1419946,2839893,5679786,11359573,22719146,
%U 45438293,90876586,181753173,363506346,727012693,1454025386,2908050773,5816101546,11632203093
%N Decimal 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="/A266248/b266248.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 (2,1,-2).
%F From _Colin Barker_, Dec 28 2015 and Apr 14 2019: (Start)
%F a(n) = (65*2^n-8*((-1)^n+3))/48 for n>3.
%F a(n) = 2*a(n-1)+a(n-2)-2*a(n-3) for n>6.
%F G.f.: (1+x^5-x^6) / ((1-x)*(1+x)*(1-2*x)).
%F (End)
%F a(n) = floor(65*2^n/48). - _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],2],{k,1,rows}] (* Binary Representation of Middle Column *)
%o (Python) print([65*2**n//48 for n in range(50)]) # _Karl V. Keller, Jr._, Dec 15 2021
%Y Cf. A266243, A266247.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 25 2015
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