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A267804
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Binary representation of the n-th iteration of the "Rule 214" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 111, 10111, 1100111, 101110111, 11001100111, 1011101110111, 110011001100111, 10111011101110111, 1100110011001100111, 101110111011101110111, 11001100110011001100111, 1011101110111011101110111, 110011001100110011001100111, 10111011101110111011101110111
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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 22 2016 and Apr 20 2019: (Start)
a(n) = 10001*a(n-2)-10000*a(n-4) for n>3.
G.f.: (1+111*x+110*x^2-10000*x^3) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).
(End)
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MATHEMATICA
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rule=214; 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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