A241509 Number of partitions of n such that (number parts having multiplicity 1) is not a part and (number of 1s) is not a part.

1, 0, 2, 2, 3, 2, 4, 5, 9, 10, 16, 20, 27, 31, 48, 53, 72, 92, 118, 143, 186, 220, 288, 356, 434, 523, 675, 792, 989, 1205, 1469, 1754, 2165, 2565, 3133, 3752, 4498, 5345, 6496, 7629, 9126, 10869, 12890, 15212, 18114, 21220, 25163, 29611, 34783, 40756, 48058

Offset

0,3

Links

Table of n, a(n) for n=0..50.

Formula

a(n) + A241510(n) = A000041(n) for n >= 0.

Example

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

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, A241507, A241508, A241510, A000041.

Sequence in context: A305894 A305811 A239471 * A268327 A053023 A153725

Adjacent sequences: A241506 A241507 A241508 * A241510 A241511 A241512

Keyword

nonn,easy

Author

Clark Kimberling, Apr 24 2014

Status

approved