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A000347 Number of partitions into non-integral powers.
(Formerly M3929 N1616)
1
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Nov 14 2010
STATUS
approved

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Last modified July 14 14:54 EDT 2024. Contains 374318 sequences. (Running on oeis4.)