A267054 - OEIS

%I #21 Jun 13 2022 14:51:21

%S 1,11,10100,101111,101010000,1010111111,1010101000000,10101011111111,

%T 10101010100000000,101010101111111111,101010101010000000000,

%U 1010101010111111111111,1010101010101000000000000,10101010101011111111111111,10101010101010100000000000000

%N Binary representation of the n-th iteration of the "Rule 93" elementary cellular automaton starting with a single ON (black) cell.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

%H Robert Price, <a href="/A267054/b267054.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 10 2016 and Apr 19 2019: (Start)

%F a(n) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>5.

%F G.f.: (1+11*x-x^2-10000*x^3-100000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).

%F (End)

%t rule=93; 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. A267053, A267055.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 09 2016

%E Removed an unjustified claim that _Colin Barker_'s conjectures are correct. Removed a program based on a conjecture. - _Michael De Vlieger_, Jun 13 2022