A241390 Number of partitions p of n such that the number of distinct parts is not a part and max(p) - min(p) is not a part.

1, 0, 1, 1, 3, 3, 6, 8, 12, 15, 22, 31, 37, 56, 67, 92, 116, 156, 190, 255, 310, 406, 498, 638, 787, 988, 1212, 1517, 1856, 2290, 2802, 3441, 4158, 5099, 6166, 7460, 9015, 10879, 13049, 15716, 18752, 22469, 26798, 31961, 37890, 45148, 53376, 63253, 74626

Offset

0,5

Links

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

Formula

a(n) + A241391(n) = A000041(n) for n >= 0.

Example

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

Mathematica

z = 40; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := d[p] = Length[DeleteDuplicates[p]];
Table[Count[f[n], p_ /; MemberQ[p, d[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241387 *)
Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241388 *)
Table[Count[f[n], p_ /; MemberQ[p, d[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241389 *)
Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241390 *)
Table[Count[f[n], p_ /; MemberQ[p, d[p]] || MemberQ[p, Max[p] - Min[p]]], {n, 0, z}]  (* A241391 *)

Crossrefs

Cf. A241387, A241388, A241389, A241391, A000041.

Sequence in context: A309455 A168637 A372887 * A241831 A239946 A130780

Adjacent sequences: A241387 A241388 A241389 * A241391 A241392 A241393

Keyword

nonn,easy

Author

Clark Kimberling, Apr 21 2014

Status

approved