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%I #32 Jul 06 2023 12:56:14
%S 1,6,3,124,3,2044,3,32764,3,524284,3,8388604,3,134217724,3,2147483644,
%T 3,34359738364,3,549755813884,3,8796093022204,3,140737488355324,3,
%U 2251799813685244,3,36028797018963964,3,576460752303423484,3,9223372036854775804,3
%N Decimal representation of the n-th iteration of the "Rule 47" elementary cellular automaton starting with a single ON (black) cell.
%H Robert Price, <a href="/A266661/b266661.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 03 2016 and Apr 18 2019: (Start)
%F a(n) = (7*(-1)^n+2^(2*n+1)-(-1)^n*2^(2*n+1)-1)/2 for n>1.
%F a(n) = 17*a(n-2)-16*a(n-4) for n>5.
%F G.f.: (1+6*x-14*x^2+22*x^3-32*x^4+32*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
%F (End)
%F a(n) = A266255(n), n>1. - _R. J. Mathar_, Jan 10 2016
%F Conjecture: a(n) = 2*4^n - 4 for odd n > 1; a(n) = 3 for even n > 1. - _Karl V. Keller, Jr._, Oct 10 2021
%t rule=47; 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. A266255, A266659, A266660.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 02 2016
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