A266607 - OEIS

%I #25 Feb 16 2025 08:33:28

%S 1,6,2,125,4,2043,8,32759,16,524271,32,8388575,64,134217663,128,

%T 2147483519,256,34359738111,512,549755813375,1024,8796093021183,2048,

%U 140737488353279,4096,2251799813681151,8192,36028797018955775,16384,576460752303407103,32768

%N Decimal representation of the n-th iteration of the "Rule 39" elementary cellular automaton starting with a single ON (black) cell.

%H Robert Price, <a href="/A266607/b266607.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://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 02 2016 and Apr 18 2019: (Start)

%F a(n) = 19*a(n-2)-50*a(n-4)+32*a(n-6) for n>5.

%F G.f.: (1+6*x-17*x^2+11*x^3+16*x^4-32*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-2*x^2)).

%F (End)

%t rule=39; 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 Cf. A266605, A266606.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 01 2016

%E Removed an unjustified claim that _Colin Barker_'s conjectures are correct. Removed a program based on a conjecture. - _N. J. A. Sloane_, Jun 13 2022