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%I #25 Sep 16 2021 02:34:18
%S 1,100,10011,1001111,100111111,10011111111,1001111111111,
%T 100111111111111,10011111111111111,1001111111111111111,
%U 100111111111111111111,10011111111111111111111,1001111111111111111111111,100111111111111111111111111,10011111111111111111111111111
%N Binary representation of the n-th iteration of the "Rule 139" elementary cellular automaton starting with a single ON (black) cell.
%H Robert Price, <a href="/A267523/b267523.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>, Wolfram Media, 2002; p. 55.
%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_02">Index entries for linear recurrences with constant coefficients</a>, signature (101,-100).
%F From _Colin Barker_, Jan 16 2016: (Start)
%F a(n) = 101*a(n-1)-100*a(n-2) for n>2.
%F G.f.: (1-x+11*x^2) / ((1-x)*(1-100*x)).
%F (End)
%F a(n) = 100^n + floor(100^(n-1)/9). - _Karl V. Keller, Jr._, Sep 15 2021
%t rule=139; 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[FromDigits[catri[[k]]],{k,1,rows}] (* Binary Representation of Rows *)
%o (Python) print([100**n + int(100**(n-1))//9 for n in range(50)]) # _Karl V. Keller, Jr._, Sep 15 2021
%Y Cf. A267520.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 16 2016
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