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A266718
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Decimal representation of the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
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3
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1, 5, 6, 123, 12, 2039, 24, 32751, 48, 524255, 96, 8388543, 192, 134217599, 384, 2147483391, 768, 34359737855, 1536, 549755812863, 3072, 8796093020159, 6144, 140737488351231, 12288, 2251799813677055, 24576, 36028797018947583, 49152, 576460752303390719, 98304
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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 04 2016 and Apr 18 2019: (Start)
a(n) = 19*a(n-2)-50*a(n-4)+32*a(n-6) for n>6.
G.f.: (1-2*x)*(1+7*x+x^2+30*x^3+8*x^4-32*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-2*x^2)).
(End)
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MATHEMATICA
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rule=59; 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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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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