A240491 Number of partitions p of n such that the multiplicity of the mean of p is a part of p.

0, 1, 0, 0, 1, 0, 1, 0, 2, 2, 4, 0, 9, 0, 8, 11, 15, 0, 39, 0, 44, 45, 28, 0, 175, 30, 50, 146, 207, 0, 486, 0, 427, 415, 144, 378, 1736, 0, 236, 1084, 2669, 0, 3022, 0, 3279, 4977, 600, 0, 12557, 1195, 6503, 5959, 11042, 0, 17047, 12549, 25925, 12977, 2174

Offset

0,9

Comments

a(n) = 0 if and only if n is a prime or 0.

Links

Table of n, a(n) for n=0..58.

Example

a(1) counts these 4 partitions:  52111, 42211, 33211, 32221.

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: A144412 A360603 A337299 * A113750 A355204 A282627

Adjacent sequences: A240488 A240489 A240490 * A240492 A240493 A240494

Keyword

nonn,easy

Author

Clark Kimberling, Apr 06 2014

Status

approved