OFFSET
1,2
FORMULA
Let q (h) be the number of partitions of h>=1 into distinct parts, as in A000009. There are q(h)^2 ways to choose the sets {x(1),...,x(j)} and {y(1),...,y(k)} each having sum h. Consequently, there are q(1)^2 + q(2)^2 + ... + q(n)^2 partitions of 0 as described in the Name section.
EXAMPLE
0 = 1-1 = 2-2 = 3-3 = 3-(1+2) = (1+2)-3 = (1+2)-(1+2),
so that a(3) = 6.
MATHEMATICA
p[n_] := PartitionsQ[Range[1, n]]; l[n_] := Length[p[n]];
s[n_] := Apply[Plus, p[n]^2];
Table[s[n], {n, 1, 45}] (* A029536 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Mar 10 2012
STATUS
approved