A000158 Number of partitions into non-integral powers.

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

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

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).

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.
• 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. [Annotated scanned copy]

Crossrefs

Cf. A000148, A000160, A000234. - R. J. Mathar, Jul 03 2009

Extensions

More terms from Sean A. Irvine, Oct 11 2009