%I #24 Jun 13 2022 21:11:53
%S 1,5,2,123,4,2039,8,32751,16,524255,32,8388543,64,134217599,128,
%T 2147483391,256,34359737855,512,549755812863,1024,8796093020159,2048,
%U 140737488351231,4096,2251799813677055,8192,36028797018947583,16384,576460752303390719,32768
%N Decimal representation of the n-th iteration of the "Rule 27" 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="/A266461/b266461.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_, Dec 31 2015 and Apr 16 2019: (Start)
%F a(n) = 19*a(n-2)-50*a(n-4)+32*a(n-6) for n>5.
%F G.f.: (1+5*x-17*x^2+28*x^3+16*x^4-48*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-2*x^2)).
%F (End)
%F Conjecture: a(n) = 2*(4^n - 2^floor(n/2)) - 1 for odd n; a(n) = 2^(n/2) for even n. - _Karl V. Keller, Jr._, Sep 29 2021
%t rule=27; 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. A266459, A266460.
%K nonn,easy
%O 0,2
%A _Robert Price_, Dec 29 2015