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A267514
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Binary representation of the middle column of the "Rule 137" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 10, 101, 1010, 10101, 101010, 1010100, 10101001, 101010010, 1010100101, 10101001010, 101010010101, 1010100101010, 10101001010100, 101010010101001, 1010100101010010, 10101001010100101, 101010010101001010, 1010100101010010101, 10101001010100101010
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OFFSET
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0,2
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
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LINKS
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FORMULA
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a(n) = 10*a(n-1)+a(n-7)-10*a(n-8) for n>7.
G.f.: (1-x+x^2)*(1+x+x^2) / ((1-x)*(1-10*x)*(1+x+x^2+x^3+x^4+x^5+x^6)).
(End)
This conjectured linear recurrence fails to predict the correct values from a(62) on. - R. J. Mathar, Apr 12 2019
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MATHEMATICA
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rule=137; 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 *)
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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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