A266671 - OEIS

%I #27 Jul 06 2023 12:57:46

%S 1,3,8,95,64,1791,512,30719,4096,507903,32768,8257535,262144,

%T 133169151,2097152,2139095039,16777216,34292629503,134217728,

%U 549218942975,1073741824,8791798054911,8589934592,140703128616959,68719476736,2251524935778303,549755813888

%N Decimal representation of the n-th iteration of the "Rule 53" elementary cellular automaton starting with a single ON (black) cell.

%H Robert Price, <a href="/A266671/b266671.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>, 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 03 2016 and Apr 18 2019: (Start)

%F a(n) = 25*a(n-2) - 152*a(n-4) + 128*a(n-6) for n>5.

%F G.f.: (1+3*x-17*x^2+20*x^3+16*x^4-128*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-8*x^2)).

%F (End)

%t rule=53; 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. A266669, A266670.

%K nonn

%O 0,2

%A _Robert Price_, Jan 02 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