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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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<.... [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009]
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REFERENCES
| 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
| B. K. Agarwala, F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.
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EXAMPLE
| 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. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009]
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CROSSREFS
| Sequence in context: A037166 A118892 A100691 * A006802 A068055 A162740
Adjacent sequences: A000295 A000296 A000297 * A000299 A000300 A000301
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| 3 more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009
More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Nov 11 2010
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