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A266724
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Number of OFF (white) cells in 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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0, 1, 3, 1, 7, 1, 11, 1, 15, 1, 19, 1, 23, 1, 27, 1, 31, 1, 35, 1, 39, 1, 43, 1, 47, 1, 51, 1, 55, 1, 59, 1, 63, 1, 67, 1, 71, 1, 75, 1, 79, 1, 83, 1, 87, 1, 91, 1, 95, 1, 99, 1, 103, 1, 107, 1, 111, 1, 115, 1, 119, 1, 123, 1, 127, 1, 131, 1, 135, 1, 139, 1
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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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Conjectures from Colin Barker, Jan 05 2016 and Apr 18 2019: (Start)
a(n) = (-1)^n*(n-1)+n for n>0.
a(n) = 2*a(n-2)-a(n-4) for n>4.
G.f.: x*(1+3*x-x^2+x^3) / ((1-x)^2*(1+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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}] (* Number of White cells in stage n *)
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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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