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 A267705 Binary representation of the n-th iteration of the "Rule 205" elementary cellular automaton starting with a single ON (black) cell. 3
 1, 10, 10101, 1101011, 111010111, 11110101111, 1111101011111, 111111010111111, 11111110101111111, 1111111101011111111, 111111111010111111111, 11111111110101111111111, 1111111111101011111111111, 111111111111010111111111111, 11111111111110101111111111111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 Index entries for sequences related to cellular automata Index to Elementary Cellular Automata FORMULA Conjectures from Colin Barker, Jan 20 2016 and Apr 20 2019: (Start) a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3) for n>3. G.f.: (1-101*x+10101*x^2-10100*x^3) / ((1-x)*(1-10*x)*(1-100*x)). (End) MATHEMATICA rule=205; 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. A267704, A188530. Sequence in context: A101305 A001098 A266872 * A086164 A138119 A327233 Adjacent sequences: A267702 A267703 A267704 * A267706 A267707 A267708 KEYWORD nonn,easy AUTHOR Robert Price, Jan 19 2016 STATUS approved

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Last modified August 13 11:02 EDT 2024. Contains 375130 sequences. (Running on oeis4.)