A267847 - OEIS

%I #20 Apr 18 2019 11:27:48

%S 1,4,26,122,506,2042,8186,32762,131066,524282,2097146,8388602,

%T 33554426,134217722,536870906,2147483642,8589934586,34359738362,

%U 137438953466,549755813882,2199023255546,8796093022202,35184372088826,140737488355322,562949953421306

%N Decimal representation of the n-th iteration of the "Rule 227" 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="/A267847/b267847.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_, Jan 21 2016: (Start)

%F a(n) = 5*a(n-1)-4*a(n-2) for n>3.

%F G.f.: (1-x+10*x^2+8*x^3) / ((1-x)*(1-4*x)).

%F (End)

%F Conjecture: a(n) = 2*(4^n - 3) for n>1. - _Colin Barker_, Nov 26 2016

%t rule=227; 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. A267845.

%K nonn

%O 0,2

%A _Robert Price_, Jan 21 2016