%I A000234 M2730 N1095
%S A000234 1,3,8,18,37,72,136,251,445,770,1312,2202,3632,5908,9501,15111,23781,
%T A000234 37083,57293,87813,133530,201574,302265,450317,666743,981488,1437003,
%U A000234 2092976,3033253,4375104,6282026,8981046,12786327,18131492,25612628
%N A000234 Partitions into non-integral powers (see Comments for precise definition).
%C A000234 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
%D A000234 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000234 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000234 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.
%e A000234 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) }.
%p A000234 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
%Y A000234 Sequence in context: A055278 A036628 A004035 this_sequence A136376 A099845 
               A036635
%Y A000234 Adjacent sequences: A000231 A000232 A000233 this_sequence A000235 A000236 
               A000237
%K A000234 nonn
%O A000234 1,2
%A A000234 N. J. A. Sloane (njas(AT)research.att.com).
%E A000234 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 19 2007
%E A000234 One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), May 03 
               2008
%E A000234 a(20)-a(35) from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Jan 17 2009