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A000397
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Number of partitions into non-integral powers.
(Formerly M4212 N1757)
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1
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6, 32, 109, 288, 654, 1337, 2506, 4414, 7379, 11822, 18273, 27356, 39938, 56974, 79607, 109267, 147523, 196295, 257715, 334407, 429086, 545034, 685917, 855886, 1059360, 1301776, 1588321, 1925620, 2320544, 2780468, 3314007, 3930001, 4638319, 5449943, 6376505, 7430471, 8625369, 9976540, 11498855, 13210238, 15128487, 17272896, 19664754, 22326319, 25280987, 28554486, 32173404, 36166409, 40563607, 45397395, 50701682, 56512012, 62866699, 69805531, 77370606, 85607286, 94560129, 104280410, 114819255, 126229853, 138570284, 151899428, 166278945, 181775849, 198456941, 216394746, 235661505, 256338017, 278503009, 302242623, 327644632, 354799834, 383805368, 414759214, 447764499, 482931051
(list; graph; refs; listen; history; internal format)
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OFFSET
| 5,1
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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 distinct integers 1<=x_1<x_2<x_3. - R. J. Mathar, Jul 03 2009
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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).
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LINKS
| 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
| A000397 := proc(n) local a, x1, x2, x3 ; a := 0 ; for x1 from 1 to n^2 do for x2 from x1+1 to floor( (n-x1^(1/2))^2 ) do x3 := (n-x1^(1/2)-x2^(1/2))^2 ; if floor(x3) >= x2+1 then a := a+floor(x3-x2) ; fi; od: od: a ; end: for n from 5 do printf("%d, \n", A000397(n)) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 29 2009]
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CROSSREFS
| Sequence in context: A177082 A090382 A102359 * A200765 A130410 A202807
Adjacent sequences: A000394 A000395 A000396 * A000398 A000399 A000400
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 29 2009
More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Nov 14 2010
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