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A000234
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Partitions into non-integral powers (see Comments for precise definition).
(Formerly M2730 N1095)
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1
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1, 3, 8, 18, 37, 72, 136, 251, 445, 770, 1312, 2202, 3632, 5908, 9501, 15111, 23781, 37083, 57293, 87813, 133530, 201574, 302265, 450317, 666743, 981488, 1437003, 2092976, 3033253, 4375104, 6282026, 8981046, 12786327, 18131492, 25612628
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This gives the number of solutions to the inequality sum_{i=1,2,..} xi^(2/3) <= n with the constraint that 1<=x1<=x2<=x3<=... is a list of at least 1 and no more than n integers. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 19 2007
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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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EXAMPLE
| a(3)=8 counts 5 partitions with 1 term, explictly { 1^(2/3), 2^(2/3), 3^(2/3), 4^(2/3), 5^(2/3)}, 2 partitions into sums of 2 terms { 1^(2/3)+1^(2/3), 1^(2/3)+2^(2/3) } and one partition into a sum of three terms { 1^(2/3)+1^(2/3)+1^(2/3) }.
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MAPLE
| fs:=n->floor(simplify(n)): a:=proc(i, m, k) options remember: local s, l, j, m2: if(k=1) then RETURN(1) else s:=0: l:=fs(m^(3/2)): for j from 1 to min(l, i) do m2:=m-j^(2/3): if(fs(m2)>=1) then s:=s+a(j, m2, k-1) fi: s:=s+1 od: RETURN(s) fi: end: seq(a(fs(n^(3/2)), n, n), n=1..19); - Herman Jamke (hermanjamke(AT)fastmail.fm), May 03 2008
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CROSSREFS
| Sequence in context: A036628 A004035 A169763 * A136376 A099845 A036635
Adjacent sequences: A000231 A000232 A000233 * A000235 A000236 A000237
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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), Oct 19 2007
One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), May 03 2008
a(20)-a(35) from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Jan 17 2009
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