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A000160 Number of partitions into non-integral powers.
(Formerly M1835 N0729)
2
1, 2, 8, 21, 48, 99, 186, 330, 556, 895, 1397, 2107, 3097, 4459, 6264, 8644, 11760, 15742, 20790, 27128, 34993, 44664, 56473, 70784, 87995, 108564, 132970, 161828, 195686, 235274, 281349, 334682, 396202, 466849, 547712, 639935, 744716, 863443 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

COMMENTS

a(n) counts the solutions to the inequality x_1^(2/3)+x_2^(2/3)+x_3^(2/3)+x_4^(2/3)<=n for any four integers 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=4..41.

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

Sequence in context: A141582 A192692 A182704 * A034519 A014409 A109782

Adjacent sequences:  A000157 A000158 A000159 * A000161 A000162 A000163

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Sean A. Irvine, Oct 11 2009

STATUS

approved

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Last modified May 24 17:40 EDT 2017. Contains 286997 sequences.