%I #31 Jul 06 2023 13:07:04
%S 1,10,10101,101010,101010101,1010101010,1010101010101,10101010101010,
%T 10101010101010101,101010101010101010,101010101010101010101,
%U 1010101010101010101010,1010101010101010101010101,10101010101010101010101010,10101010101010101010101010101
%N Binary representation of the n-th iteration of the "Rule 77" elementary cellular automaton starting with a single ON (black) cell.
%H Robert Price, <a href="/A266872/b266872.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>
%F Conjectures from _Colin Barker_, Jan 05 2016 and Apr 18 2019: (Start)
%F a(n) = 10001*a(n-2) - 10000*a(n-4) for n>3.
%F G.f.: (1+10*x)*(1+100*x^2) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).
%F (End)
%t rule=77; 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. A266873.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 04 2016