cp's OEIS Frontend

A267614 Decimal representation of the n-th iteration of the "Rule 185" elementary cellular automaton starting with a single ON (black) cell.

%I A267614 #36 Jun 30 2025 13:06:15
%S A267614 1,1,11,47,191,767,3071,12287,49151,196607,786431,3145727,12582911,
%T A267614 50331647,201326591,805306367,3221225471,12884901887,51539607551,
%U A267614 206158430207,824633720831,3298534883327,13194139533311,52776558133247,211106232532991,844424930131967
%N A267614 Decimal representation of the n-th iteration of the "Rule 185" elementary cellular automaton starting with a single ON (black) cell.
%D A267614 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A267614 Robert Price, <a href="/A267614/b267614.txt">Table of n, a(n) for n = 0..1000</a>
%H A267614 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267614 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A267614 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267614 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A267614 Conjectures from _Colin Barker_, Jan 18 2016 and Apr 20 2019: (Start)
%F A267614 a(n) = 5*a(n-1) - 4*a(n-2) for n>3.
%F A267614 G.f.: (1-4*x+10*x^2-4*x^3) / ((1-x)*(1-4*x)).
%F A267614 (End)
%F A267614 Empirical a(n) = 3*4^(n-1)-1 = A198693(n-1) for n>1. - _Colin Barker_, Nov 25 2016 and Apr 20 2019
%t A267614 rule=185; 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]],2],{k,1,rows}]   (* Decimal Representation of Rows *)
%Y A267614 Cf. A198693, A267612, A267613.
%K A267614 nonn,easy
%O A267614 0,3
%A A267614 _Robert Price_, Jan 18 2016
%E A267614 Removed an unjustified claim that _Colin Barker_'s conjectures are correct. Removed a program based on a conjecture. - _Michael De Vlieger_, Jun 13 2022