A000347 Number of partitions into non-integral powers. (Formerly M3929 N1616)

1, 5, 24, 84, 251, 653, 1543, 3341, 6763, 12879, 23446, 40883, 68757, 111976, 177358, 273926, 413784, 612430, 889959, 1271709, 1789841, 2483779, 3402623, 4605954, 6166614, 8171174, 10724604, 13950011, 17994136, 23029141, 29255902, 36908235, 46257694, 57616522, 71344257, 87853381, 107612397

Offset

4,2

Comments

a(n) counts the solutions to the inequality x_1^(1/2) + x_2^(1/2) + x_3^((1/2) + x_4^(1/2) <= 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..40.

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: A274723 A006328 A213766 * A270906 A268587 A334459

Adjacent sequences: A000344 A000345 A000346 * A000348 A000349 A000350

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Nov 14 2010

Status

approved