A241733 Number of partitions p of n such that round(mean(p)) is a part of p; here, round(x) means floor(x + 1/2).

0, 1, 2, 3, 4, 5, 7, 10, 13, 18, 24, 31, 44, 57, 73, 94, 127, 166, 203, 268, 338, 424, 548, 674, 858, 1046, 1321, 1643, 1973, 2472, 3026, 3774, 4529, 5455, 6736, 8013, 9699, 11899, 14299, 16926, 20377, 24373, 29018, 34679, 41447, 48688, 57395, 68775, 81535

Offset

0,3

Comments

For the corresponding sequence using "round" as in Mathematica, see A241338.

Links

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

Formula

a(n) + A241734(n) = A000041(n) for n >= 0.

Example

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

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, A241734.

Sequence in context: A193771 A160333 A174578 * A241338 A271489 A018127

Adjacent sequences: A241730 A241731 A241732 * A241734 A241735 A241736

Keyword

nonn,easy

Author

Clark Kimberling, Apr 28 2014

Status

approved