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 A267777 Binary representation of the n-th iteration of the "Rule 209" elementary cellular automaton starting with a single ON (black) cell. 1
 1, 1, 11001, 1111001, 111111001, 11111111001, 1111111111001, 111111111111001, 11111111111111001, 1111111111111111001, 111111111111111111001, 11111111111111111111001, 1111111111111111111111001, 111111111111111111111111001, 11111111111111111111111111001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Rule 241 also generates this sequence. REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. LINKS Robert Price, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton S. Wolfram, A New Kind of Science FORMULA Conjectures from Colin Barker, Jan 20 2016 and Apr 20 2019: (Start) a(n) = 101*a(n-1)-100*a(n-2) for n>2. G.f.: (1-100*x+11000*x^2) / ((1-x)*(1-100*x)). (End) MATHEMATICA rule=209; 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]]], {k, 1, rows}]   (* Binary Representation of Rows *) CROSSREFS Cf. A267776, A141722. Sequence in context: A352751 A266983 A227865 * A034712 A178586 A045152 Adjacent sequences:  A267774 A267775 A267776 * A267778 A267779 A267780 KEYWORD nonn,easy AUTHOR Robert Price, Jan 20 2016 EXTENSIONS Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022 STATUS approved

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Last modified August 10 13:12 EDT 2022. Contains 356039 sequences. (Running on oeis4.)