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A000345 Number of partitions into non-integral powers.
(Formerly M3918 N1610)
1
1, 5, 22, 71, 186, 427, 888, 1704, 3053, 5203, 8476, 13318, 20265, 29946, 43254, 61171, 84832, 115713, 155382, 205779, 269065, 347906, 445001, 563685, 707637, 881042, 1088339, 1335019, 1626233, 1968701, 2369320, 2835467, 3375820, 3999234, 4715586, 5535965, 6472005, 7536195, 8742102, 10105163, 11640190, 13365254, 15298155, 17458190, 19866739, 22546131, 25519743, 28813410, 32453730, 36469433, 40890672, 45749944, 51081147, 56919908, 63304577, 70275008, 77873381, 86145156, 95134772, 104893757, 115473250, 126926418, 139311512, 152687434, 167115830, 182663928, 199398527, 217392226, 236717247, 257454630, 279683011, 303488723, 328959602, 356186407 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,2
COMMENTS
a(n) counts the solutions to the inequality x_1^(1/2) + x_2^(1/2) + x_3^(1/2) <= n for any three integers 1 <= x_1 <= x_2 <= x_3. - 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: A273768 A032168 A246211 * A011846 A241694 A220733
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Nov 14 2010
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)