A000333 Number of partitions into non-integral powers. (Formerly M3856 N1579)

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

Offset

1,2

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, 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=1..34.

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]

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, Jul 03 2009]

Crossrefs

Sequence in context: A132985 A022570 A152881 * A291225 A054888 A201157

Adjacent sequences: A000330 A000331 A000332 * A000334 A000335 A000336

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

More terms from Sean A. Irvine, Nov 14 2010

Status

approved