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A241334 Number of partitions p of n including floor(mean(p)) as a part. 6
0, 1, 2, 3, 4, 6, 8, 11, 15, 21, 27, 38, 48, 65, 86, 111, 140, 189, 233, 306, 383, 481, 608, 782, 936, 1186, 1481, 1828, 2223, 2793, 3331, 4144, 5012, 6079, 7437, 9051, 10586, 12970, 15738, 18851, 22161, 26885, 31644, 38188, 45142, 52983, 63328, 75823, 87404 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) + A241335(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 8 partitions:  6, 33, 321, 3111, 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. A241335, A241336, A241338, A000041, A241312.

Sequence in context: A087192 A188917 A046935 * A095814 A006683 A014213

Adjacent sequences:  A241331 A241332 A241333 * A241335 A241336 A241337

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 20 2014

STATUS

approved

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Last modified August 4 07:32 EDT 2020. Contains 336201 sequences. (Running on oeis4.)