A266460 - OEIS

%I #25 Jun 13 2022 21:11:21

%S 1,101,10,1111011,100,11111110111,1000,111111111101111,10000,

%T 1111111111111011111,100000,11111111111111110111111,1000000,

%U 111111111111111111101111111,10000000,1111111111111111111111011111111,100000000,11111111111111111111111110111111111

%N Binary representation of the n-th iteration of the "Rule 27" 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="/A266460/b266460.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_, Dec 31 2015 and Apr 16 2019: (Start)

%F a(n) = 10011*a(n-2)-110010*a(n-4)+100000*a(n-6) for n>5.

%F G.f.: (1+101*x-10001*x^2+99900*x^3+10000*x^4-110000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-10*x^2)).

%F (End)

%F Conjecture: a(n) = (10*(100^n - 9*10^floor(n/2)) - 1)/9 for odd n; a(n) = 10^(n/2) for even n. - _Karl V. Keller, Jr._, Sep 29 2021

%t rule=27; 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. A266459, A266461.

%K nonn,easy

%O 0,2

%A _Robert Price_, Dec 29 2015