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A266850
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Decimal 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, 6, 4, 123, 16, 2031, 64, 32703, 256, 524031, 1024, 8387583, 4096, 134213631, 16384, 2147467263, 65536, 34359672831, 262144, 549755551743, 1048576, 8796091973631, 4194304, 140737484161023, 16777216, 2251799796908031, 67108864, 36028796951855103, 268435456
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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) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>5.
G.f.: (1+6*x-17*x^2-3*x^3+16*x^4-48*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*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]], 2], {k, 1, rows}] (* Decimal 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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