A241443 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, 0, 1, 1, 1, 1, 2, 3, 5, 6, 10, 12, 18, 18, 31, 31, 48, 54, 72, 88, 121, 139, 185, 225, 283, 349, 439, 526, 662, 809, 970, 1183, 1478, 1723, 2125, 2553, 3071, 3659, 4438, 5228, 6306, 7476, 8896, 10522, 12590, 14709, 17501, 20602, 24290, 28455, 33592, 39163

Offset

0,7

Links

Table of n, a(n) for n=0..51.

Formula

a(n) + A241442(n) + A241444(n) = A241446(n) for n >= 0.

Example

a(6) counts these 2 partitions:  222, 2211.

Mathematica

z = 30; f[n_] := f[n] = IntegerPartitions[n]; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 1 &]]]; d[p_] := Length[DeleteDuplicates[p]];
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && MemberQ[p, d[p]]], {n, 0, z}]  (* A241442 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, d[p]] ], {n, 0,  z}] (* A241443 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241444 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241445 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, d[p]] ], {n, 0, z}] (* A241446 *)

Crossrefs

Cf. A241442, A241444, A241445, A241446.

Sequence in context: A007211 A027593 A115029 * A023025 A130898 A199016

Adjacent sequences: A241440 A241441 A241442 * A241444 A241445 A241446

Keyword

nonn,easy

Author

Clark Kimberling, Apr 23 2014

Status

approved