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A267273
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Binary representation of the n-th iteration of the "Rule 117" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 11, 11000, 11111, 110000000, 111111111, 1100000000000, 1111111111111, 11000000000000000, 11111111111111111, 110000000000000000000, 111111111111111111111, 1100000000000000000000000, 1111111111111111111111111, 11000000000000000000000000000
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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 14 2016 and Apr 19 2019: (Start)
a(n) = 10001*a(n-2)-10000*a(n-4) for n>5.
G.f.: (1+11*x+999*x^2-98900*x^3-1000*x^4+100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).
(End)
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MATHEMATICA
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rule=117; 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
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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