A241451 Number of partitions p of n such that the number of parts having multiplicity 1 is a part or max(p) - min(p) is a part.

0, 1, 0, 1, 1, 4, 6, 9, 13, 21, 28, 35, 52, 68, 89, 121, 155, 205, 264, 340, 433, 555, 693, 872, 1095, 1367, 1695, 2107, 2580, 3180, 3911, 4773, 5803, 7083, 8565, 10364, 12515, 15077, 18075, 21721, 25936, 31023, 36954, 43984, 52152, 61966, 73238, 86586

Offset

0,6

Links

Table of n, a(n) for n=0..47.

Formula

a(n) + A241450(n) = A000041(n) for n >= 0.

Example

a(6) counts these 6 partitions:  42, 411, 321, 3111, 2211, 21111.

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, A241450.

Sequence in context: A010737 A048625 A120134 * A354965 A288379 A112381

Adjacent sequences: A241448 A241449 A241450 * A241452 A241453 A241454

Keyword

nonn,easy

Author

Clark Kimberling, Apr 23 2014

Status

approved