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A086520
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Number of integers strictly greater than (n-sqrt(n))/2 and strictly less than (n+sqrt(n))/2.
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2
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0, 0, 1, 2, 1, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10
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OFFSET
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0,4
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COMMENTS
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This sequence occurs in quantum mechanics, in the context of counting certain kinds of inseparable states in an n-qubit model.
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LINKS
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EXAMPLE
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a(16) = 3 because there are three integers between 6 and 10.
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MAPLE
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a:= n-> max(0, ceil((n+sqrt(n))/2)-1-floor((n-sqrt(n))/2)):
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MATHEMATICA
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a[n_] := If[IntegerQ[Sqrt[n]], Sum[1, {m, Ceiling[(n - Sqrt[n])/2] + 1, Floor[(n + Sqrt[n])/2] - 1}], Sum[1, {m, Ceiling[(n - Sqrt[n])/2], Floor[(n + Sqrt[n])/2]}]]
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Jeff S. Pratt (jpratt(AT)pas.rochester.edu), Sep 10 2003
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EXTENSIONS
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STATUS
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approved
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