A241514 Number of partitions of n such that (number parts having multiplicity 1) is not a part and (number of parts > 1) is not a part.

1, 0, 2, 2, 2, 2, 4, 3, 8, 9, 16, 19, 30, 32, 54, 62, 86, 103, 140, 161, 224, 255, 337, 402, 520, 600, 787, 914, 1167, 1383, 1717, 2026, 2549, 2969, 3664, 4347, 5297, 6203, 7617, 8913, 10760, 12683, 15225, 17828, 21424, 25009, 29784, 34954, 41414, 48274

Offset

0,3

Links

Table of n, a(n) for n=0..49.

Formula

a(n) + A241515(n) = A000041(n) for n >= 0.

Example

a(6) counts these 4 partitions:  6, 33, 222, 111111.

Mathematica

z = 30; f[n_] := f[n] = IntegerPartitions[n]; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] ==       1 &]]];
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && MemberQ[p, Length[p] - Count[p, 1]]], {n, 0, z}]  (* A241511 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, Length[p] - Count[p, 1]] ], {n, 0, z}] (* A241512 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, Length[p] - Count[p, 1]] ], {n, 0, z}] (* A241513 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, Length[p] - Count[p, 1]] ], {n, 0, z}] (* A241514 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, Length[p] - Count[p, 1]] ], {n, 0, z}] (* A241515 *)

Crossrefs

Cf. A241506, A241511, A241511, A241512, A241513, A241515.

Sequence in context: A110884 A303637 A155904 * A125913 A122386 A051464

Adjacent sequences: A241511 A241512 A241513 * A241515 A241516 A241517

Keyword

nonn,easy

Author

Clark Kimberling, Apr 24 2014

Status

approved