A241447 Number of partitions p of n such that the number of parts having multiplicity 1 is a part and max(p) - min(p) is a part.

0, 0, 0, 1, 1, 2, 3, 3, 4, 6, 7, 9, 13, 19, 22, 29, 38, 45, 65, 75, 94, 119, 151, 181, 238, 280, 341, 419, 526, 615, 764, 920, 1097, 1335, 1605, 1902, 2285, 2733, 3233, 3873, 4586, 5376, 6386, 7556, 8845, 10436, 12234, 14322, 16812, 19623, 22806, 26692

Offset

0,6

Links

Table of n, a(n) for n=0..51.

Formula

a(n) + A241448(n) + A241449(n) = A241451(n) for n >= 0.

Example

a(6) counts these 3 partitions:  42, 321, 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. A241448, A241449, A241450, A241451.

Sequence in context: A327725 A253926 A277579 * A081230 A341144 A365831

Adjacent sequences: A241444 A241445 A241446 * A241448 A241449 A241450

Keyword

nonn,easy

Author

Clark Kimberling, Apr 23 2014

Status

approved