A241336 Number of partitions p of n including ceiling(mean(p)) as a part.

0, 1, 2, 3, 4, 5, 7, 9, 12, 16, 22, 28, 39, 49, 66, 87, 112, 141, 190, 234, 307, 384, 482, 609, 783, 937, 1187, 1482, 1829, 2224, 2794, 3332, 4145, 5013, 6080, 7438, 9052, 10587, 12971, 15739, 18852, 22162, 26886, 31645, 38189, 45143, 52984, 63329, 75824

Offset

0,3

Links

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

Formula

a(n) + A241337(n) = A000041(n) for n >= 0.

Example

a(6) counts these 7 partitions:  6, 33, 321, 222, 2211, 21111, 111111.

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, A241337, A000041, A241312.

Sequence in context: A117598 A120149 A117597 * A233522 A112639 A290137

Adjacent sequences: A241333 A241334 A241335 * A241337 A241338 A241339

Keyword

nonn,easy

Author

Clark Kimberling, Apr 20 2014

Status

approved