A000158 Number of partitions into non-integral powers. (Formerly M1830 N0726)

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

3,2

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

Table of n, a(n) for n=3..43.

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

Sequence in context: A240279 A327728 A372485 * A101427 A286269 A126877

Adjacent sequences: A000155 A000156 A000157 * A000159 A000160 A000161

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Oct 11 2009

Status

approved