OFFSET
0,3
EXAMPLE
a(6)= 9 counts all of the 11 partitions of 6 except 51, 411.
MATHEMATICA
z = 30; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := d[p] = Length[DeleteDuplicates[p]]; g[p_] := Max[-Differences[p]];
Table[Count[f[n], p_ /; g[p] < d[p]], {n, 0, z}] (* A241818 *)
Table[Count[f[n], p_ /; g[p] <= d[p]], {n, 0, z}] (* A241819 *)
Table[Count[f[n], p_ /; g[p] == d[p]], {n, 0, z}] (* A241820 *)
Table[Count[f[n], p_ /; g[p] >= d[p]], {n, 0, z}] (* A241821 *)
Table[Count[f[n], p_ /; g[p] > d[p]], {n, 0, z}] (* A241822 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 30 2014
STATUS
approved