OFFSET
0,5
COMMENTS
For each partition of n, let
d = number of terms that are not repeated;
r = number of terms that are repeated.
a(n) is the number of partitions such that d < r.
EXAMPLE
The partitions of 6 are 6, 51, 42, 411, 33, 321, 3111, 222, 2211, 21111, 111111.
These have d > r: 6, 51, 42, 321
These have d = r: 411, 3222, 21111
These have d < r: 33, 222, 2211, 111111
Thus, a(6) = 4.
MATHEMATICA
z = 30; d[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 1 &]]];
r[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]]; Table[Count[IntegerPartitions[n], p_ /; d[p] < r[p]], {n, 0, z}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 03 2020
STATUS
approved