cp's OEIS Frontend

A265688 Binary representation of the n-th iteration of the "Rule 190" elementary cellular automaton starting with a single ON (black) cell.

%I A265688 #24 Feb 16 2025 08:33:27
%S A265688 1,111,11101,1110111,111011101,11101110111,1110111011101,
%T A265688 111011101110111,11101110111011101,1110111011101110111,
%U A265688 111011101110111011101,11101110111011101110111,1110111011101110111011101,111011101110111011101110111,11101110111011101110111011101
%N A265688 Binary representation of the n-th iteration of the "Rule 190" elementary cellular automaton starting with a single ON (black) cell.
%D A265688 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A265688 Robert Price, <a href="/A265688/b265688.txt">Table of n, a(n) for n = 0..499</a>
%H A265688 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule190.html">Rule 190</a>
%H A265688 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A265688 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A265688 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A265688 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (100,1,-100).
%F A265688 From _Colin Barker_, Dec 13 2015 and Apr 18 2019: (Start)
%F A265688 a(n) = (-165*(-1)^n+37*100^(n+1)-202)/3333.
%F A265688 a(n) = (37*100^(n+1)-367)/3333 for n even.
%F A265688 a(n) = (37*100^(n+1)-37)/3333 for n odd.
%F A265688 a(n) = 100*a(n-1) + a(n-2) - 100*a(n-3) for n>2.
%F A265688 G.f.: (1+11*x) / ((1-x)*(1+x)*(1-100*x)).
%F A265688 (End)
%F A265688 a(n) = floor(11100*100^n/9999). - _Karl V. Keller, Jr._, Aug 10 2021
%t A265688 rule = 190; rows = 20; Table[FromDigits[Table[Take[CellularAutomaton[rule,{{1},0}, rows-1, {All,All}][[k]], {rows-k+1, rows+k-1}], {k,1,rows}][[k]]], {k,1,rows}]
%o A265688 (Python) print([11100*100**n//9999 for n in range(30)]) # _Karl V. Keller, Jr._, Aug 10 2021
%Y A265688 Cf. A037576 (decimal), A118111.
%K A265688 nonn,easy
%O A265688 0,2
%A A265688 _Robert Price_, Dec 13 2015