OFFSET
0,6
EXAMPLE
a(9) counts these 9 partitions: 432, 4311, 3321, 32211, 321111, 222211, 222111, 221111, 21111111.
MATHEMATICA
z = 40; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := d[p] = Length[DeleteDuplicates[p]];
Table[Count[f[n], p_ /; MemberQ[p, d[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241387 *)
Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241388 *)
Table[Count[f[n], p_ /; MemberQ[p, d[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241389 *)
Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241390 *)
Table[Count[f[n], p_ /; MemberQ[p, d[p]] || MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241391 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 21 2014
STATUS
approved