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A000298
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Number of partitions into non-integral powers.
(Formerly M3439 N1395)
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1
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1, 4, 12, 30, 70, 159, 339, 706, 1436, 2853, 5551, 10622, 19975, 37043, 67811, 122561, 219090, 387578, 678977, 1178769, 2029115, 3465056, 5872648, 9882301, 16517284, 27430358, 45275673, 74297072, 121245153, 196810381, 317850809, 510830685, 817139589, 1301251186, 2063204707, 3257690903, 5123047561
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OFFSET
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1,2
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COMMENTS
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a(n) is the number of solutions to the inequality sum_{i=1,2,..} x_i^(1/2)<=n for unknowns 1<=x_1<x_2<x_3<x_4<.... - R. J. Mathar, Jul 03 2009
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REFERENCES
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B. K. Agarwala and F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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EXAMPLE
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The 12 solutions for n=3 are 1^(1/2)<=3, 1^(1/2)+2^(1/2)<=3, 1^(1/2)+3^(1/2)<=3, 1^(1/2)+4^(1/2)<=3, 2^(1/2)<=3, 3^(1/2)<=3,...,8^(1/2)<=3 and 9^(1/2)<=3. - R. J. Mathar, Jul 03 2009
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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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