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Search: id:A000158
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| A000158 |
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Number of partitions into non-integral powers.
(Formerly M1830 N0726)
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+0
2
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| 1, 2, 8, 19, 41, 78, 134, 218, 339, 506, 730, 1023, 1397, 1884, 2477, 3218, 4118, 5192, 6486, 8010, 9795, 11888, 14302, 17066, 20256, 23889, 27999, 32637, 37863, 43695, 50218, 57495, 65545, 74431, 84257, 95030, 106840, 119799, 133941, 149311, 166071
(list; graph; listen)
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OFFSET
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3,2
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COMMENT
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a(n) counts the solutions to the inequality x_1^(2/3)+x_2^(2/3)+x_3^(2/3)<=n for any three integers 1<=x_1<=x_2<=x_3. - R. J. Mathar, Jul 03 2009
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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LINKS
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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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CROSSREFS
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Cf. A000148, A000160, A000234. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009]
Adjacent sequences: A000155 A000156 A000157 this_sequence A000159 A000160 A000161
Sequence in context: A109071 A031327 A030504 this_sequence A101427 A126877 A107769
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KEYWORD
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nonn,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Oct 11 2009
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