

A000345


Number of partitions into nonintegral 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
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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 nonintegral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207216.
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 nonintegral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207216.
B. K. Agarwala and F. C. Auluck, Statistical mechanics and partitions into nonintegral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207216. [Annotated scanned copy]


CROSSREFS

Sequence in context: A273768 A032168 A246211 * A011846 A241694 A220733
Adjacent sequences: A000342 A000343 A000344 * A000346 A000347 A000348


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Sean A. Irvine, Nov 14 2010


STATUS

approved



