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A000333
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Number of partitions into non-integral powers.
(Formerly M3856 N1579)
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0
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1, 5, 15, 40, 98, 237, 534, 1185, 2554, 5391, 11117, 22556, 44858, 88000, 170107, 324547, 611755, 1140382, 2103554, 3842826, 6955918, 12483075, 22220002, 39248230, 68819781, 119839422, 207304370, 356356801, 608901907, 1034452712, 1747764522, 2937370605, 4911675955, 8173032301
(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=1,2,3...} x_i^(1/2)<=n under the constraint that x_i are integers where 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
| a(n=3)=15 counts the solutions 1^(1/2)<=3, 1^(1/2)+1^(1/2)<=3, 1^(1/2)+1^(1/2)+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, 2^(1/2)+2^(1/2)<=3, 3^(1/2)<=3, 4^(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: A132985 A022570 A152881 * A201157 A054888 A038066
Adjacent sequences: A000330 A000331 A000332 * A000334 A000335 A000336
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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
| 2 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 14 2010
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