OFFSET
1,2
COMMENTS
Number of partitions of n whose rank is not 0.
EXAMPLE
For n = 5 we have:
-------------------------------------------------------
Partitions Largest Number Dyson's
of 5 part of parts rank Type
-------------------------------------------------------
5 5 - 1 = 4 unbalanced
4+1 4 - 2 = 2 unbalanced
3+2 3 - 2 = 1 unbalanced
3+1+1 3 - 3 = 0 balanced
2+2+1 2 - 3 = -1 unbalanced
2+1+1+1 2 - 4 = -2 unbalanced
1+1+1+1+1 1 - 5 = -4 unbalanced
-------------------------------------------------------
There are 6 partitions whose rank is not 0, so a(5) = 6.
MATHEMATICA
P = PartitionsP;
a[n_] := P[n] - Sum[-(-1)^k (P[n - (3k^2 - k)/2] - P[n - (3k^2 + k)/2]), {k, 1, Floor[(1 + Sqrt[1 + 24n])/6]}];
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 18 2014
STATUS
approved