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A244860
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Number of Fibonacci numbers in generation n of the tree at A232559.
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1
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1, 1, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 1, 1, 1, 0, 3, 0, 1, 1, 1, 2, 0, 0, 2, 0, 1, 1, 1, 2, 1, 0, 0, 3, 2, 0, 1, 1, 0, 0, 1, 1, 0, 4, 1, 0, 1, 0, 0, 1, 4, 2, 0, 1, 0, 1, 0, 1, 2, 1, 1, 0, 3, 0, 1, 0, 1, 1, 1, 2, 1, 0, 2, 3, 0, 1, 0, 0, 1, 0, 3, 0, 1, 0, 1, 1, 2
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OFFSET
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1,4
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COMMENTS
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Generation n consists of F(n) = A000045(n) distinct Fibonacci numbers. Is {a(n)} bounded above?
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LINKS
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EXAMPLE
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In the table below, g(n) denotes generation n of the tree at A232559.
n ... g(n) ............ a(n)
1 ... {1} ............. 1
2 ... {2} ............. 1
3 ... {3,4} ........... 1
4 ... {5,6,8} ......... 2
5 ... {7,9,10,12,16} .. 0
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MATHEMATICA
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z = 32; g[1] = {1}; f1[x_] := f1[x] = x + 1; f2[x_] := f2[x] = 2 x; h[1] = g[1]; b[n_] := b[n] = DeleteDuplicates[Union[f1[g[n - 1]], f2[g[n - 1]]]]; h[n_] := h[n] = Union[h[n - 1], g[n - 1]]; g[n_] := g[n] = Complement [b[n], Intersection[b[n], h[n]]]; f = Table[Fibonacci[n], {n, 1, 90}]; Table[Length[Intersection[g[n], f]], {n, 1, z}]
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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