A000298 Number of partitions into non-integral powers.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(n) is the number of solutions to the inequality sum_{i=1,2,..} x_i^(1/2)<=n for unknowns 1<=x_1R. J. Mathar, Jul 03 2009

Examples

			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. - _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]

Extensions

3 more terms from R. J. Mathar, Jul 03 2009

More terms from Sean A. Irvine, Nov 11 2010