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A266849
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Binary representation of the n-th iteration of the "Rule 71" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 110, 100, 1111011, 10000, 11111101111, 1000000, 111111110111111, 100000000, 1111111111011111111, 10000000000, 11111111111101111111111, 1000000000000, 111111111111110111111111111, 100000000000000, 1111111111111111011111111111111, 10000000000000000
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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 05 2016 and Apr 18 2019: (Start)
a(n) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>5.
G.f.: (1+110*x-10001*x^2-99*x^3+10000*x^4-110000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).
(End)
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MATHEMATICA
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rule=71; 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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