A241512 Number of partitions of n such that (number parts having multiplicity 1) is not a part and (number of parts > 1) is a part.

0, 0, 0, 0, 2, 1, 2, 4, 4, 4, 5, 8, 9, 10, 13, 14, 21, 24, 31, 41, 52, 67, 89, 110, 134, 182, 219, 280, 337, 429, 523, 640, 785, 959, 1168, 1416, 1714, 2083, 2482, 2971, 3596, 4282, 5103, 6079, 7236, 8555, 10176, 11958, 14129, 16668, 19545, 22949, 26939

Offset

0,5

Links

Table of n, a(n) for n=0..52.

Formula

a(n) + A241511(n) + A241513(n) = A241515(n) for n >= 0.

Example

a(6) counts these 2 partitions:  51, 2211.

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, A241513, A241514, A241515.

Sequence in context: A349816 A105970 A133950 * A360095 A350659 A094265

Adjacent sequences: A241509 A241510 A241511 * A241513 A241514 A241515

Keyword

nonn,easy

Author

Clark Kimberling, Apr 24 2014

Status

approved