1,2

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

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.

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) }.

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

Sequence in context: A055278 A036628 A004035 this_sequence A136376 A099845 A036635

Adjacent sequences: A000231 A000232 A000233 this_sequence A000235 A000236 A000237

nonn

N. J. A. Sloane (njas(AT)research.att.com).

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