%I #21 Feb 16 2025 08:33:29
%S 1,6,5,122,21,2026,85,32682,341,523946,1365,8387242,5461,134212266,
%T 21845,2147461802,87381,34359650986,349525,549755464362,1398101,
%U 8796091624106,5592405,140737482762922,22369621,2251799791315626,89478485,36028796929485482,357913941
%N Decimal representation of the n-th iteration of the "Rule 79" 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="/A266980/b266980.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="https://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 18 2019: (Start)
%F a(n) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>5.
%F G.f.: (1+6*x-16*x^2-4*x^3-32*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).
%F (End)
%t rule=79; 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. A266978, A266979.
%K nonn,easy,changed
%O 0,2
%A _Robert Price_, Jan 07 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