A241507 Number of partitions of n such that (number parts having multiplicity 1) is not a part and (number of 1s) is a part.

0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 5, 7, 12, 11, 19, 23, 35, 35, 53, 59, 90, 102, 138, 156, 220, 259, 331, 402, 515, 607, 771, 912, 1169, 1363, 1699, 2011, 2513, 2941, 3603, 4255, 5230, 6096, 7438, 8695, 10546, 12344, 14797, 17301, 20760, 24186, 28783, 33566

Offset

0,7

Links

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

Formula

a(n) + A241506(n) + A241508(n) = A241510(n) for n >= 0.

Example

a(6) counts these 3 partitions:  42, 411, 2111.

Mathematica

z = 52; 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, Count[p, 1]]], {n, 0, z}]  (* A241506 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241507 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241508 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241509 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, Count[p, 1]] ], {n, 0, z}] (* A241510 *)

Crossrefs

Cf. A241506, A241508, A241509, A241510.

Sequence in context: A354485 A055501 A096010 * A243927 A102330 A103598

Adjacent sequences: A241504 A241505 A241506 * A241508 A241509 A241510

Keyword

nonn,easy

Author

Clark Kimberling, Apr 24 2014

Status

approved