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A241336 Number of partitions p of n including ceiling(mean(p)) as a part. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 18 08:47 EDT 2020. Contains 337166 sequences. (Running on oeis4.)