A240492 Number of partitions p of n such that the multiplicity of the median of p is a part of p.

0, 1, 0, 0, 2, 1, 2, 2, 7, 8, 13, 13, 22, 25, 37, 46, 69, 80, 116, 138, 187, 226, 301, 363, 481, 585, 750, 912, 1163, 1404, 1768, 2132, 2654, 3199, 3948, 4743, 5823, 6976, 8496, 10158, 12306, 14656, 17661, 20986, 25154, 29814, 35578, 42042, 49996, 58930

Offset

0,5

Links

Table of n, a(n) for n=0..49.

Example

a(8) counts these 7 partitions:  521, 431, 422, 41111, 332, 3221, 32111.

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 - A240495.

Sequence in context: A023140 A145859 A145863 * A110775 A229232 A092186

Adjacent sequences: A240489 A240490 A240491 * A240493 A240494 A240495

Keyword

nonn,easy

Author

Clark Kimberling, Apr 06 2014

Status

approved