A240495 Number of partitions p of n such that the multiplicity of (max(p) - min(p)) is a part.

0, 0, 0, 1, 1, 1, 2, 2, 5, 5, 8, 10, 16, 19, 25, 33, 46, 53, 72, 89, 114, 141, 183, 217, 278, 339, 421, 510, 632, 759, 931, 1124, 1361, 1636, 1977, 2354, 2830, 3378, 4034, 4781, 5695, 6732, 7975, 9420, 11098, 13063, 15376, 18014, 21124, 24716, 28883, 33697

Offset

0,7

Links

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

Example

a(8) counts these 5 partitions:  431, 422, 3221, 32111, 22211.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Mean[p]]]], {n, 0, z}]  (* A240491 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Median[p]]]], {n, 0, z}]  (* A240492 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Min[p]]]], {n, 0, z}]  (* A240493 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Max[p]]]], {n, 0, z}]  (* A240494 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, Max[p] - Min[p]]]], {n, 0, z}]  (* A240495 *)

Crossrefs

Cf. A240491 - A240494.

Sequence in context: A091609 A183563 A222706 * A304393 A325535 A345165

Adjacent sequences: A240492 A240493 A240494 * A240496 A240497 A240498

Keyword

nonn,easy

Author

Clark Kimberling, Apr 06 2014

Status

approved