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A267210
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Decimal representation of the middle column of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 3, 7, 14, 29, 59, 118, 237, 475, 950, 1901, 3803, 7606, 15213, 30427, 60854, 121709, 243419, 486838, 973677, 1947355, 3894710, 7789421, 15578843, 31157686, 62315373, 124630747, 249261494, 498522989, 997045979, 1994091958, 3988183917, 7976367835
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listen;
history;
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internal format)
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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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Conjectures from Colin Barker, Jan 13 2016 and Apr 19 2019: (Start)
a(n) = 2*a(n-1)+a(n-3)-2*a(n-4) for n>3.
G.f.: (1+x+x^2-x^3) / ((1-x)*(1-2*x)*(1+x+x^2)).
(End)
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MATHEMATICA
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rule=109; 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], 2], {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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