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Search: id:A000263
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| A000263 |
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Number of partitions into non-integral powers.
(Formerly M2967 N1200)
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+0
1
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| 3, 14, 39, 91, 173, 307, 502, 779, 1150, 1651, 2280, 3090, 4090, 5313, 6787, 8564, 10643, 13103, 15948, 19235, 23000, 27316, 32174, 37677, 43849, 50758, 58427, 66978, 76373, 86765, 98171, 110662, 124310, 139202, 155339, 172885
(list; graph; listen)
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OFFSET
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3,1
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COMMENT
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a(n) counts the solutions to the inequality x_1^(1/2)+x_2^(1/2)<=n for any two distinct integers 1<=x_1<x_2. - R. J. Mathar, Jul 03 2009
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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LINKS
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B. K. Agarwala, F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.
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MAPLE
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A000263 := proc(n) local a, x1, x2 ; a := 0 ; for x1 from 1 to n^2 do x2 := (n-x1^(1/2))^2 ; if floor(x2) >= x1+1 then a := a+floor(x2-x1) ; fi; od: a ; end: seq(A000263(n), n=3..80) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 29 2009]
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CROSSREFS
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Sequence in context: A143941 A162147 A027444 this_sequence A102590 A034130 A005701
Adjacent sequences: A000260 A000261 A000262 this_sequence A000264 A000265 A000266
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 29 2009
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