A266516 - OEIS

%I #24 Jun 13 2022 21:13:28

%S 1,3,4,111,16,1983,64,32511,256,523263,1024,8384511,4096,134201343,

%T 16384,2147418111,65536,34359476223,262144,549754765311,1048576,

%U 8796088827903,4194304,140737471578111,16777216,2251799746576383,67108864,36028796750528511,268435456

%N Decimal representation of the n-th iteration of the "Rule 29" elementary cellular automaton starting with a single ON (black) cell.

%H Robert Price, <a href="/A266516/b266516.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>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,21,0,-84,0,64).

%F Empirical a(n) = 21*a(n-2) - 84*a(n-4) + 64*a(n-6) for n>5. - _Vincenzo Librandi_, Dec 31 2015 and Apr 16 2019

%F Empirical g.f.: (1+3*x-17*x^2+48*x^3+16*x^4-96*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)). - _Colin Barker_, Dec 31 2015 and Apr 16 2019

%F Conjecture: a(n) = 2*(4^n - 2^n) - 1 for odd n; a(n) = 2^n for even n. - _Karl V. Keller, Jr._, Oct 03 2021

%t rule=29; 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. A266514, A266515.

%K nonn,easy

%O 0,2

%A _Robert Price_, Dec 30 2015