A241386 Number of partitions p of n such that the number of parts is a part or max(p) - min(p) is a part.

0, 1, 0, 1, 2, 4, 4, 8, 10, 15, 19, 24, 35, 45, 57, 76, 98, 123, 161, 198, 252, 313, 388, 472, 597, 722, 891, 1085, 1332, 1602, 1964, 2348, 2852, 3412, 4109, 4889, 5879, 6964, 8317, 9846, 11706, 13795, 16358, 19226, 22695, 26630, 31305, 36621, 42966, 50116

Offset

0,5

Links

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

Formula

a(n) + A241385(n) = A000041(n) for n >= 0.

Example

a(6) counts these 4 partitions:  42, 321, 2211, 21111.

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, A241385.

Sequence in context: A342695 A039879 A125204 * A265204 A073420 A034408

Adjacent sequences: A241383 A241384 A241385 * A241387 A241388 A241389

Keyword

nonn,easy

Author

Clark Kimberling, Apr 21 2014

Status

approved