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Search: id:A000327
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| A000327 |
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Number of partitions into non-integral powers.
(Formerly M3819 N1563)
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+0
1
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| 1, 5, 12, 23, 39, 62, 91, 127, 171, 228, 294, 370, 461, 561, 677, 811, 955, 1121, 1303, 1499, 1719, 1960, 2218, 2499, 2806, 3131, 3485, 3868, 4274, 4706, 5166, 5658, 6175, 6725, 7309, 7923, 8572, 9256, 9972, 10728, 11521, 12349, 13218, 14126, 15072
(list; graph; listen)
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OFFSET
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3,2
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COMMENT
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a(n) counts the solutions to the inequality x_1^(2/3)+x_2^(2/3)<=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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A000327 := proc(n) local a, x1, x2 ; a := 0 ; for x1 from 1 to floor(n^(3/2)) do x2 := (n-x1^(2/3))^(3/2) ; if floor(x2) >= x1+1 then a := a+floor(x2-x1) ; fi; od: a ; end: seq(A000327(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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Adjacent sequences: A000324 A000325 A000326 this_sequence A000328 A000329 A000330
Sequence in context: A025740 A054307 A126573 this_sequence A130624 A066869 A023172
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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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