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A266508
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Binary representation of the n-th iteration of the "Rule 28" elementary cellular automaton starting with a single ON (black) cell.
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6
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1, 11, 101, 1011, 10101, 101011, 1010101, 10101011, 101010101, 1010101011, 10101010101, 101010101011, 1010101010101, 10101010101011, 101010101010101, 1010101010101011, 10101010101010101, 101010101010101011, 1010101010101010101, 10101010101010101011
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OFFSET
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0,2
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COMMENTS
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Rule 156 also generates this sequence.
Also, the binary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 678", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. See A283641.
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LINKS
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FORMULA
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a(n) = (44 - 45*(-1)^n + 10^(2+n))/99.
a(n) = 10*a(n-1) + a(n-2) - 10*a(n-3) for n>2.
G.f.: (1+x-10*x^2) / ((1-x)*(1+x)*(1-10*x)).
(End)
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MATHEMATICA
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rule=28; 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 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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