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A048006
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Number of nonempty subsets of {1,2,...,n} in which exactly 1/3 of the elements are <= (n-1)/3.
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1
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0, 0, 0, 3, 6, 10, 25, 45, 77, 175, 322, 570, 1245, 2325, 4213, 9031, 17061, 31421, 66547, 126763, 236203, 496063, 950818, 1787346, 3730293, 7184421, 13598053, 28243063, 54604081, 103918153, 215008363, 416990563, 797154723
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = Sum_{k=1..floor(n/3)} binomial(floor((n-1)/3), 3*k)*binomial(ceiling(2*(n-1)/3), 2*k). - Robert Israel, Feb 05 2017
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MAPLE
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f:= n -> add(binomial(floor((n-1)/3), k/3)*binomial(n-floor((n-1)/3),
2*k/3), k=3..n, 3):
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PROG
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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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