A241513 Number of partitions of n such that (number parts having multiplicity 1) is a part and (number of parts > 1) is not a part.

0, 1, 0, 0, 0, 0, 0, 2, 1, 4, 4, 9, 12, 24, 25, 44, 57, 84, 109, 159, 193, 277, 344, 458, 571, 763, 923, 1211, 1474, 1874, 2305, 2902, 3494, 4399, 5314, 6543, 7907, 9733, 11609, 14198, 16993, 20539, 24512, 29557, 35032, 42082, 49858, 59373, 70194, 83490

Offset

0,8

Links

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

Formula

a(n) + A241511(n) + A241512(n) = A241515(n) for n >= 0.

Example

a(10) counts these 4 partitions:  631, 5221, 42211, 32221.

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, A241514, A241515.

Sequence in context: A355020 A008346 A119282 * A095293 A034409 A209478

Adjacent sequences: A241510 A241511 A241512 * A241514 A241515 A241516

Keyword

nonn,easy

Author

Clark Kimberling, Apr 24 2014

Status

approved