A241378 Number of partitions of n such that the number of parts is not a part and the number of distinct parts is a part.

0, 0, 1, 1, 2, 3, 3, 5, 7, 10, 14, 18, 27, 32, 49, 58, 80, 100, 134, 167, 219, 271, 351, 433, 543, 689, 848, 1051, 1298, 1609, 1945, 2413, 2930, 3566, 4321, 5266, 6302, 7647, 9156, 11022, 13174, 15770, 18752, 22408, 26606, 31498, 37375, 44205, 52143, 61507

Offset

0,5

Links

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

Formula

a(n) + A241377(n) + A241379(n) = A241381(n) for n >= 0.

Example

a(9) counts these 10 partitions:  522, 3321, 3222, 32211, 321111, 22221, 222111, 221111, 211111, 111111111.

Mathematica

z = 30; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := [p] = Length[DeleteDuplicates[p]];
Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && MemberQ[p, d[p]]], {n, 0, z}]  (* A241377 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && MemberQ[p, d[p]]], {n, 0, z}]  (* A241378 *)
Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && ! MemberQ[p, d[p]]], {n, 0, z}]  (* A241379 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && ! MemberQ[p, d[p]]], {n, 0, z}]  (* A241380 *)
Table[Count[f[n], p_ /; MemberQ[p, Length[p]] || MemberQ[p, d[p]]], {n, 0, z}] (* A241381 *)

Crossrefs

Cf. A241377, A241379, A241380, A241381.

Sequence in context: A108961 A017984 A286330 * A226275 A035066 A258967

Adjacent sequences: A241375 A241376 A241377 * A241379 A241380 A241381

Keyword

nonn,easy

Author

Clark Kimberling, Apr 21 2014

Status

approved