A241734 Number of partitions p of n such that round(mean(p)) is not a part of p; here, round(x) means floor(x + 1/2).

1, 0, 0, 0, 1, 2, 4, 5, 9, 12, 18, 25, 33, 44, 62, 82, 104, 131, 182, 222, 289, 368, 454, 581, 717, 912, 1115, 1367, 1745, 2093, 2578, 3068, 3820, 4688, 5574, 6870, 8278, 9738, 11716, 14259, 16961, 20210, 24156, 28582, 33728, 40446, 48163, 55979, 657385

Offset

0,6

Comments

For the corresponding sequence using "round" as in Mathematica, see A241339.

Links

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

Formula

a(n) + A241733(n) = A000041(n) for n >= 0.

Example

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

Mathematica

z = 40; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p] + 1/2]]], {n, 0, z}]   (* A241733 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p] + 1/2]]], {n, 0, z}]   (* A241734 *)

Crossrefs

Cf. A241338, A241733.

Sequence in context: A327781 A241411 A211373 * A371171 A039898 A083690

Adjacent sequences: A241731 A241732 A241733 * A241735 A241736 A241737

Keyword

nonn,easy

Author

Clark Kimberling, Apr 28 2014

Status

approved