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%I #32 Jul 06 2023 13:10:57
%S 1,5,8,111,64,1919,512,31743,4096,516095,32768,8323071,262144,
%T 133693439,2097152,2143289343,16777216,34326183935,134217728,
%U 549487378431,1073741824,8793945538559,8589934592,140720308486143,68719476736,2251662374731775,549755813888
%N Decimal representation of the n-th iteration of the "Rule 83" elementary cellular automaton starting with a single ON (black) cell.
%H Robert Price, <a href="/A267003/b267003.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 08 2016 and Apr 19 2019: (Start)
%F a(n) = 25*a(n-2)-152*a(n-4)+128*a(n-6) for n>5.
%F G.f.: (1+2*x)*(1+3*x-23*x^2+32*x^3-48*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-8*x^2)).
%F (End)
%t rule=83; 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. A267001, A267002.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 08 2016
%E Removed an unjustified claim that _Colin Barker_'s conjectures are correct. Removed a program based on a conjecture. - _Michael De Vlieger_, Jun 13 2022
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