A241385 Number of partitions p of n such that the number of parts is not a part and max(p) - min(p) is not a part.

1, 0, 2, 2, 3, 3, 7, 7, 12, 15, 23, 32, 42, 56, 78, 100, 133, 174, 224, 292, 375, 479, 614, 783, 978, 1236, 1545, 1925, 2386, 2963, 3640, 4494, 5497, 6731, 8201, 9994, 12098, 14673, 17698, 21339, 25632, 30788, 36816, 44035, 52480, 62504, 74253, 88133, 104307

Offset

0,3

Links

Table of n, a(n) for n=0..48.

Formula

a(n) + A241386(n) = A000041(n) for n >= 0.

Example

a(6) counts these 7 partitions:  6, 51, 411, 33, 3111, 222, 111111.

Mathematica

z = 40; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241382 *)
Table[Count[f[n],  p_ /; ! MemberQ[p, Length[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241383 *)
Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241384 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241385 *)
Table[Count[f[n], p_ /; MemberQ[p, Length[p]] || MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241386 *)

Crossrefs

Cf. A241382, A241383, A241384, A241386.

Sequence in context: A309684 A330950 A032060 * A307736 A309713 A153903

Adjacent sequences: A241382 A241383 A241384 * A241386 A241387 A241388

Keyword

nonn,easy

Author

Clark Kimberling, Apr 21 2014

Status

approved