A241450 Number of partitions p of n such that the number of parts having multiplicity 1 is not a part and max(p) - min(p) is not a part.

1, 0, 2, 2, 4, 3, 5, 6, 9, 9, 14, 21, 25, 33, 46, 55, 76, 92, 121, 150, 194, 237, 309, 383, 480, 591, 741, 903, 1138, 1385, 1693, 2069, 2546, 3060, 3745, 4519, 5462, 6560, 7940, 9464, 11402, 13560, 16220, 19277, 23023, 27168, 32320, 38168, 45184, 53120

Offset

0,3

Links

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

Formula

a(n) + A241451(n) = A000041(n) for n >= 0.

Example

a(6) counts these 5 partitions:  6, 51, 33, 222, 111111.

Mathematica

z = 30; f[n_] := f[n] = IntegerPartitions[n]; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 1 &]]]; d[p_] := Length[DeleteDuplicates[p]];
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && MemberQ[p, Max[p]-Min[p]]], {n, 0, z}]  (* A241447 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && MemberQ[p, Max[p]-Min[p]] ], {n, 0,  z}] (* A241448 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] && ! MemberQ[p, Max[p]-Min[p]] ], {n, 0, z}] (* A241449 *)
Table[Count[f[n], p_ /; ! MemberQ[p, u[p]] && ! MemberQ[p, Max[p]-Min[p]] ], {n, 0, z}] (* A241450 *)
Table[Count[f[n], p_ /; MemberQ[p, u[p]] || MemberQ[p, Max[p]-Min[p]] ], {n, 0, z}] (* A241451 *)

Crossrefs

Cf. A241447, A241448, A241449, A241451.

Sequence in context: A329436 A182577 A357189 * A189675 A248746 A227154

Adjacent sequences: A241447 A241448 A241449 * A241451 A241452 A241453

Keyword

nonn,easy

Author

Clark Kimberling, Apr 23 2014

Status

approved