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A266674
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Decimal representation of the n-th iteration of the "Rule 57" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 1, 10, 75, 76, 1623, 600, 29295, 4784, 496351, 37728, 8164799, 300736, 132422527, 2403712, 2133112575, 19192576, 34244750847, 153466368, 548835613695, 1227582464, 8788730820607, 9818265600, 140678589542399, 78541336576, 2251328604004351, 628321116160
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OFFSET
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0,3
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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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Empirical g.f.: (1 +x -17*x^2 +40*x^3 -64*x^5 -248*x^6 +128*x^7 +1472*x^8 -2048*x^10) / ((1 -x)*(1 +x)*(1 -2*x)*(1 -4*x)*(1 +4*x)*(1 -2*x^2)*(1 +2*x +4*x^2)*(1 -8*x^2)). - Colin Barker, Jan 03 2016 and Apr 18 2019
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MATHEMATICA
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rule=57; 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
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AUTHOR
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STATUS
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approved
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