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A266670
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Binary representation of the n-th iteration of the "Rule 53" elementary cellular automaton starting with a single ON (black) cell.
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3
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1, 11, 1000, 1011111, 1000000, 11011111111, 1000000000, 111011111111111, 1000000000000, 1111011111111111111, 1000000000000000, 11111011111111111111111, 1000000000000000000, 111111011111111111111111111, 1000000000000000000000, 1111111011111111111111111111111
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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 03 2016 and Apr 16 2019: (Start)
a(n) = 11001*a(n-2) - 10011000*a(n-4) + 10000000*a(n-6) for n>5.
G.f.: (1+11*x-10001*x^2+890100*x^3+10000*x^4-2000000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-1000*x^2)).
(End)
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MATHEMATICA
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rule=53; 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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EXTENSIONS
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Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - N. J. A. Sloane, Jun 13 2022
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STATUS
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approved
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