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%I #29 Jul 06 2023 13:22:33
%S 1,2,15,63,255,1023,4095,16383,65535,262143,1048575,4194303,16777215,
%T 67108863,268435455,1073741823,4294967295,17179869183,68719476735,
%U 274877906943,1099511627775,4398046511103,17592186044415,70368744177663,281474976710655
%N Decimal representation of the n-th iteration of the "Rule 173" elementary cellular automaton starting with a single ON (black) cell.
%H Robert Price, <a href="/A267596/b267596.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 18 2016 and Apr 20 2019: (Start)
%F a(n) = 5*a(n-1)-4*a(n-2) for n>3.
%F G.f.: (1-3*x+9*x^2-4*x^3) / ((1-x)*(1-4*x)).
%F (End)
%F Empirical a(n) = 4^n - 1 for n>1. - _Colin Barker_, Nov 25 2016 and Apr 20 2019
%t rule=173; 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. A267594, A267595.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 18 2016