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A267775
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Binary representation of the n-th iteration of the "Rule 207" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 110, 11101, 1111011, 111110111, 11111101111, 1111111011111, 111111110111111, 11111111101111111, 1111111111011111111, 111111111110111111111, 11111111111101111111111, 1111111111111011111111111, 111111111111110111111111111, 11111111111111101111111111111
(list;
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refs;
listen;
history;
text;
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 20 2016 and Apr 20 2019: (Start)
a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3) for n>3.
G.f.: (1-x+x^2-100*x^3) / ((1-x)*(1-10*x)*(1-100*x)).
(End)
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MATHEMATICA
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rule=207; 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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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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