A000298 - OEIS

A000298

Number of partitions into non-integral powers.
(Formerly M3439 N1395)

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

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OFFSET

1,2

COMMENTS

a(n) is the number of solutions to the inequality sum_{i=1,2,..} x_i^(1/2)<=n for unknowns 1<=x_1<x_2<x_3<x_4<.... - 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..37.

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

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

CROSSREFS

Sequence in context: A118892 A036388 A100691 * A218009 A249914 A006802

Adjacent sequences: A000295 A000296 A000297 * A000299 A000300 A000301

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

More terms from Sean A. Irvine, Nov 11 2010

STATUS

approved