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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

Table of n, a(n) for n=3..76.

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

Adjacent sequences:  A000342 A000343 A000344 * A000346 A000347 A000348

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Sean A. Irvine, Nov 14 2010

STATUS

approved

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Last modified August 18 12:24 EDT 2017. Contains 290720 sequences.