A241448 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 a part.

0, 0, 0, 0, 0, 0, 1, 1, 3, 4, 7, 6, 14, 9, 21, 21, 31, 35, 50, 52, 82, 85, 117, 129, 174, 191, 265, 291, 366, 427, 547, 597, 788, 868, 1087, 1244, 1549, 1726, 2159, 2420, 2954, 3405, 4108, 4630, 5637, 6396, 7640, 8744, 10359, 11822, 14087, 15989, 18779

Offset

0,9

Links

Table of n, a(n) for n=0..52.

Formula

a(n) + A241447(n) + A241449(n) = A241451(n) for n >= 0.

Example

a(6) counts this single partition:  2211.

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, A241449, A241450, A241451.

Sequence in context: A053480 A258052 A344484 * A323243 A346193 A244974

Adjacent sequences: A241445 A241446 A241447 * A241449 A241450 A241451

Keyword

nonn,easy

Author

Clark Kimberling, Apr 23 2014

Status

approved