OFFSET
0,4
EXAMPLE
a(6) counts these 5 partitions: 41, 321, 2211, 21111, 111111.
MATHEMATICA
z = 30; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := [p] = Length[DeleteDuplicates[p]];
Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && MemberQ[p, d[p]]], {n, 0, z}] (* A241377 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && MemberQ[p, d[p]]], {n, 0, z}] (* A241378 *)
Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && ! MemberQ[p, d[p]]], {n, 0, z}] (* A241379 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && ! MemberQ[p, d[p]]], {n, 0, z}] (* A241380 *)
Table[Count[f[n], p_ /; MemberQ[p, Length[p]] || MemberQ[p, d[p]]], {n, 0, z}] (* A241381 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 21 2014
STATUS
approved