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 A266720 Binary representation of the middle column of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell. 3
 1, 10, 101, 1011, 10110, 101101, 1011010, 10110101, 101101010, 1011010101, 10110101010, 101101010101, 1011010101010, 10110101010101, 101101010101010, 1011010101010101, 10110101010101010, 101101010101010101, 1011010101010101010, 10110101010101010101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Robert Price, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. Index entries for sequences related to cellular automata Index to Elementary Cellular Automata Index entries for linear recurrences with constant coefficients, signature (10,1,-10). FORMULA From Colin Barker, Jan 04 2016 and Apr 18 2019: (Start) a(n) = (-450*(-1)^n+10009*10^n-550)/9900 for n>1. a(n) = 10*a(n-1)+a(n-2)-10*a(n-3) for n>4. G.f.: (1+x^3-x^4) / ((1-x)*(1+x)*(1-10*x)). (End) a(n) = floor(10009*10^n/9900). - Karl V. Keller, Jr., Oct 17 2021 MATHEMATICA rule=59; 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 *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc, k]], {k, 1, rows}] (* Binary Representation of Middle Column *) PROG (Python) print([10009*10**n//9900 for n in range(50)]) # Karl V. Keller, Jr., Oct 18 2021 CROSSREFS Cf. A266716, A266719, A266721. Sequence in context: A284137 A284179 A096883 * A033128 A094945 A190480 Adjacent sequences: A266717 A266718 A266719 * A266721 A266722 A266723 KEYWORD nonn,easy AUTHOR Robert Price, Jan 03 2016 STATUS approved

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Last modified May 27 23:16 EDT 2024. Contains 372900 sequences. (Running on oeis4.)