A241449 Number of partitions p of n such that the number of parts having multiplicity 1 is a part and max(p) - min(p) is not a part.

0, 1, 0, 0, 0, 2, 2, 5, 6, 11, 14, 20, 25, 40, 46, 71, 86, 125, 149, 213, 257, 351, 425, 562, 683, 896, 1089, 1397, 1688, 2138, 2600, 3256, 3918, 4880, 5873, 7218, 8681, 10618, 12683, 15428, 18396, 22242, 26460, 31798, 37670, 45134, 53364, 63520, 74918

Offset

0,6

Links

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

Formula

a(n) + A241447(n) + A241448(n) = A241451(n) for n >= 0.

Example

a(6) counts these 2 partitions:  411, 3111.

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, A241450, A241451.

Sequence in context: A288766 A348324 A007988 * A240184 A317853 A238517

Adjacent sequences: A241446 A241447 A241448 * A241450 A241451 A241452

Keyword

nonn,easy

Author

Clark Kimberling, Apr 23 2014

Status

approved