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A000345
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Number of partitions into non-integral powers.
(Formerly M3918 N1610)
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1
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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
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3,2
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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