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%I #26 Jun 13 2022 20:57:33
%S 1,5,19,95,319,1535,5119,24575,81919,393215,1310719,6291455,20971519,
%T 100663295,335544319,1610612735,5368709119,25769803775,85899345919,
%U 412316860415,1374389534719,6597069766655,21990232555519,105553116266495,351843720888319
%N Decimal representation of the n-th iteration of the "Rule 155" 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="/A263245/b263245.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 20 2016 and Apr 17 2019: (Start)
%F a(n) = a(n-1)+16*a(n-2)-16*a(n-3) for n>3.
%F G.f.: (1+4*x-2*x^2+12*x^3) / ((1-x)*(1-4*x)*(1+4*x)).
%F (End)
%F Empirical a(n) = (11*4^n-(-4)^n-8)/8 for n>0. - _Colin Barker_, Nov 25 2016 and Apr 17 2019
%F Conjecture: a(n) = 3*4^((n-1)/2)*2^n - 1 for odd n; a(n) = 5*4^(n/2 - 1)*2^n - 1 for even n > 0. - _Karl V. Keller, Jr._, May 01 2022
%t rule=155; 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 *)
%o (
%Y Cf. A263243, A263244.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 17 2016
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