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A267879
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Binary representation of the middle column of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 10, 101, 1010, 10101, 101011, 1010111, 10101111, 101011111, 1010111111, 10101111111, 101011111111, 1010111111111, 10101111111111, 101011111111111, 1010111111111111, 10101111111111111, 101011111111111111, 1010111111111111111, 10101111111111111111
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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) = 11*a(n-1)-10*a(n-2) for n>4.
G.f.: (1-x+x^2-x^3+x^4) / ((1-x)*(1-10*x)).
(End)
Conjecture: a(n) = (9091*10^(n-3) - 1)/9 for n > 2. - Stefano Spezia, Dec 25 2021
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MATHEMATICA
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rule=233; 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 *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc, k]], {k, 1, rows}] (* Binary Representation of Middle Column *)
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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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