A241410 Number of partitions of n such that the number of parts having multiplicity >1 is not a part and the number of distinct parts is a part.

0, 1, 0, 1, 0, 1, 2, 2, 4, 5, 7, 8, 12, 17, 22, 29, 33, 49, 59, 77, 97, 123, 153, 199, 234, 306, 375, 460, 557, 708, 845, 1048, 1266, 1548, 1852, 2282, 2698, 3303, 3919, 4732, 5634, 6786, 7991, 9598, 11343, 13502, 15897, 18912, 22180, 26298, 30775, 36259

Offset: 0

Author

Clark Kimberling, Apr 22 2014

Keywords

• nonn
• easy

Comments

As used here, the term "distinct parts" includes each number, once, that occurs more than once; e.g., the distinct parts of the partition {4,3,3,1,1,1} are 4, 3, 1.

Examples

			a(6) counts these 2 partitions: 42, 321.
		

Crossrefs

Cf. A241408, A241409, A241411, A241412.

Programs

Mathematica

z = 30; f[n_] := f[n] = IntegerPartitions[n]; e[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]]; d[p_] := Length[DeleteDuplicates[p]];
Table[Count[f[n], p_ /; MemberQ[p, e[p]]], {n, 0, z}]  (* A241408 *)
Table[Count[f[n], p_ /; MemberQ[p, e[p]] && MemberQ[p, d[p]]], {n, 0, z}]  (* A241409 *)
Table[Count[f[n], p_ /; ! MemberQ[p, e[p]] && MemberQ[p, d[p]] ], {n, 0, z}] (* A241410 *)
Table[Count[f[n], p_ /; MemberQ[p, e[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241411  *)
Table[Count[f[n], p_ /; ! MemberQ[p, e[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241412  *)