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A266846
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Decimal representation of the n-th iteration of the "Rule 70" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 6, 20, 104, 336, 1696, 5440, 27264, 87296, 436736, 1397760, 6989824, 22368256, 111845376, 357908480, 1789558784, 5726601216, 28633071616, 91625881600, 458129670144, 1466015154176, 7330076819456, 23456246661120, 117281237499904, 375299963355136
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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 05 2016 and Apr 18 2019: (Start)
a(n) = 2^(n-1)*(-(-2)^n+9*2^n-2)/3 = 2^(n-1)*A061547(n+3).
a(n) = 2*a(n-1)+16*a(n-2)-32*a(n-3) for n>2.
G.f.: (1+4*x-8*x^2) / ((1-2*x)*(1-4*x)*(1+4*x)).
(End)
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MATHEMATICA
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rule=70; 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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