|
%I #23 Jun 13 2022 21:36:50
%S 1,110,10100,1101000,101010000,11010100000,1010101000000,
%T 110101010000000,10101010100000000,1101010101000000000,
%U 101010101010000000000,11010101010100000000000,1010101010101000000000000,110101010101010000000000000,10101010101010100000000000000
%N Binary representation of the n-th iteration of the "Rule 70" elementary cellular automaton starting with a single ON (black) cell.
%C Rule 198 also generates this sequence.
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H Robert Price, <a href="/A266844/b266844.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 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</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>
%F Conjectures from _Colin Barker_, Jan 05 2016 and Apr 18 2019: (Start)
%F a(n) = (2^(n-1)*(-9*(-50)^n-2*5^n+209*50^n))/99.
%F a(n) = 10*a(n-1)+10000*a(n-2)-100000*a(n-3) for n>2.
%F G.f.: (1+100*x-1000*x^2) / ((1-10*x)*(1-100*x)*(1+100*x)).
%F (End)
%t rule=70; 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 *)
%Y Cf. A266843, A266846.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 04 2016
| 