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%I #32 Aug 27 2023 13:16:23
%S 1,110,11000,1100000,110000000,11000000000,1100000000000,
%T 110000000000000,11000000000000000,1100000000000000000,
%U 110000000000000000000,11000000000000000000000,1100000000000000000000000,110000000000000000000000000,11000000000000000000000000000
%N Binary representation of the n-th iteration of the "Rule 14" elementary cellular automaton starting with a single ON (black) cell.
%C Rules 46, 142 and 174 also generate this sequence.
%H Robert Price, <a href="/A266299/b266299.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 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_01">Index entries for linear recurrences with constant coefficients</a>, signature (100).
%F From _Colin Barker_, Dec 28 2015 and Apr 14 2019: (Start)
%F a(n) = 11*10^(2*n-1) for n>0.
%F a(n) = 100*a(n-1) for n>1.
%F G.f.: (1+10*x) / (1-100*x).
%F (End)
%F a(n) = floor(110*100^(n-1)). - _Karl V. Keller, Jr._, Aug 30 2021
%t rule=14; 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 *)
%t LinearRecurrence[{100},{1,110},20] (* _Harvey P. Dale_, Aug 27 2023 *)
%o (Python) print([int(110*100**(n-1)) for n in range(50)]) # _Karl V. Keller, Jr._, Aug 30 2021
%Y Cf. A164908, A266298.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 26 2015
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