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

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,more

njas

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