A241337 Number of partitions p of n not including ceiling(mean(p)) as a part.

1, 0, 0, 0, 1, 2, 4, 6, 10, 14, 20, 28, 38, 52, 69, 89, 119, 156, 195, 256, 320, 408, 520, 646, 792, 1021, 1249, 1528, 1889, 2341, 2810, 3510, 4204, 5130, 6230, 7445, 8925, 11050, 13044, 15446, 18486, 22421, 26288, 31616, 36986, 43991, 52574, 61425, 71449

Offset

0,6

Links

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

Example

a(6) counts these 4 partitions:  51, 42, 411, 3111.

Mathematica

z = 30; f[n_] := f[n] = IntegerPartitions[n];
    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241334 *)
    Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241335 *)
    Table[Count[f[n], p_ /; MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241336 *)
    Table[Count[f[n], p_ /; ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241337 *)
    Table[Count[f[n], p_ /; MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241338 *)
    Table[Count[f[n], p_ /; ! MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241339 *)

Crossrefs

Cf. A241334, A241335, A241336, A000041, A241312.

Sequence in context: A000123 A268752 A277277 * A103257 A103259 A280131

Adjacent sequences: A241334 A241335 A241336 * A241338 A241339 A241340

Keyword

nonn,easy

Author

Clark Kimberling, Apr 20 2014

Status

approved