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A267456
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Binary representation of the n-th iteration of the "Rule 133" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 10, 100, 1000, 1010100, 10101000, 10101010100, 101010101000, 101010101010100, 1010101010101000, 1010101010101010100, 10101010101010101000, 10101010101010101010100, 101010101010101010101000, 101010101010101010101010100, 1010101010101010101010101000
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OFFSET
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0,2
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LINKS
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FORMULA
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Conjectures from Colin Barker, Jan 15 2016 and Apr 19 2019: (Start)
a(n) = 10001*a(n-2) - 10000*a(n-4) for n > 5.
G.f.: (1+10*x)*(1 - 9901*x^2 + 20000*x^4) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).
(End)
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MATHEMATICA
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rule=133; 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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STATUS
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approved
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