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 A267623 Binary representation of the middle column of the "Rule 187" elementary cellular automaton starting with a single ON (black) cell. 4
 1, 10, 101, 1011, 10111, 101111, 1011111, 10111111, 101111111, 1011111111, 10111111111, 101111111111, 1011111111111, 10111111111111, 101111111111111, 1011111111111111, 10111111111111111, 101111111111111111, 1011111111111111111, 10111111111111111111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also, The binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 643", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. See A283508. 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 19 2016 and Apr 16 2019: (Start) a(n) = 11*a(n-1)-10*a(n-2) for n>2. G.f.: (1-x+x^2) / ((1-x)*(1-10*x)). (End) Empirical: a(n) = (91*10^n - 10) / 90 for n>0. - Colin Barker, Mar 10 2017 It also appears that a(n) = floor(91*10^n/90). - Karl V. Keller, Jr., May 28 2022 MAPLE # Rule 187: value in generation r and column c, where c=0 is the central one r187 := proc(r::integer, c::integer) option remember; local up ; if r = 0 then if c = 0 then 1; else 0; end if; else # previous 3 bits [procname(r-1, c+1), procname(r-1, c), procname(r-1, c-1)] ; up := op(3, %)+2*op(2, %)+4*op(1, %) ; # rule 187 = 10111011_2: {6, 2}->0, all others ->1 if up in {6, 2} then 0; else 1 ; end if; end if; end proc: A267623 := proc(n) b := [seq(r187(r, 0), r=0..n)] ; add(op(-i, b)*2^(i-1), i=1..nops(b)) ; A007088(%) ; end proc: smax := 30 ; L := [seq(A267623(n), n=0..smax)] ; # R. J. Mathar, Apr 12 2019 MATHEMATICA rule=187; 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 *) CROSSREFS Cf. A267621, A283508, A083329. Sequence in context: A033128 A094945 A190480 * A283508 A261200 A175541 Adjacent sequences: A267620 A267621 A267622 * A267624 A267625 A267626 KEYWORD nonn,easy AUTHOR Robert Price, Jan 18 2016 EXTENSIONS Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - N. J. A. Sloane, Jun 13 2022 STATUS approved

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Last modified May 20 11:25 EDT 2024. Contains 372712 sequences. (Running on oeis4.)