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%I #20 Jun 13 2022 21:25:15
%S 1,1,24,31,384,511,6144,8191,98304,131071,1572864,2097151,25165824,
%T 33554431,402653184,536870911,6442450944,8589934591,103079215104,
%U 137438953471,1649267441664,2199023255551,26388279066624,35184372088831,422212465065984,562949953421311
%N Decimal representation of the n-th iteration of the "Rule 81" 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="/A266984/b266984.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 08 2016 and Apr 17 2019: (Start)
%F a(n) = ((-4)^n+(-1)^n-1)/2+4^n for n>0.
%F a(n) = 17*a(n-2)-16*a(n-4) for n>4.
%F G.f.: (1+2*x)*(1-x+9*x^2-4*x^3) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
%F (End)
%t rule=81; 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. A266982, A266983.
%K nonn,easy
%O 0,3
%A _Robert Price_, Jan 07 2016