A266718 - OEIS

%I #31 Jul 06 2023 12:59:59

%S 1,5,6,123,12,2039,24,32751,48,524255,96,8388543,192,134217599,384,

%T 2147483391,768,34359737855,1536,549755812863,3072,8796093020159,6144,

%U 140737488351231,12288,2251799813677055,24576,36028797018947583,49152,576460752303390719,98304

%N Decimal representation of the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.

%H Robert Price, <a href="/A266718/b266718.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 04 2016 and Apr 18 2019: (Start)

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

%F G.f.: (1-2*x)*(1+7*x+x^2+30*x^3+8*x^4-32*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-2*x^2)).

%F (End)

%t rule=59; 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. A266716, A266717.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 03 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