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Search: id:A102366
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| A102366 |
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Number of subsets of {1,2,...,n} in which exactly half of the elements are less than or equal to sqrt(n). |
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+0
1
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| 1, 1, 2, 3, 6, 10, 15, 21, 28, 84, 120, 165, 220, 286, 364, 455, 1820, 2380, 3060, 3876, 4845, 5985, 7315, 8855, 10626, 53130, 65780, 80730, 98280, 118755, 142506, 169911, 201376, 237336, 278256, 324632, 1947792, 2324784, 2760681, 3262623, 3838380
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n) = Sum_k C(floor[sqrt(n)], k)*C(n-floor[sqrt(n)], k) =A048093(n)+1 =a(n-1)+A084919(n-1)
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EXAMPLE
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a(5)=10 since the ten subsets of {1,2,3,4,5} are { }, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {1,2, 3,4}, {1,2, 3,5}, and {1,2, 4,5}.
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CROSSREFS
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Cf. A011782 for number of subsets with an even number of elements.
Adjacent sequences: A102363 A102364 A102365 this_sequence A102367 A102368 A102369
Sequence in context: A084396 A090035 A111467 this_sequence A074134 A056178 A018141
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Feb 22 2005
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