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%I #28 Jul 06 2023 12:29:45
%S 1,3,7,47,95,703,1407,11007,22015,175103,350207,2797567,5595135,
%T 44744703,89489407,715849727,1431699455,11453333503,22906667007,
%U 183252287487,366504574975,2932032405503,5864064811007,46912501710847,93825003421695,750599960264703
%N Decimal representation of the n-th iteration of the "Rule 157" elementary cellular automaton starting with a single ON (black) cell.
%H Robert Price, <a href="/A263806/b263806.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 20 2016 and Apr 17 2019: (Start)
%F a(n) = 3*a(n-1)+14*a(n-2)-48*a(n-3)+32*a(n-4) for n>4.
%F G.f.: (1-16*x^2+32*x^3-32*x^4) / ((1-x)*(1-2*x)*(1-4*x)*(1+4*x)).
%F (End)
%t rule=157; 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. A263804, A263805.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 17 2016
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