A241316 Number of partitions p of n into distinct parts, including round(mean(p)).

0, 1, 1, 2, 1, 2, 2, 3, 2, 4, 4, 5, 5, 7, 7, 10, 10, 13, 15, 17, 19, 25, 27, 31, 35, 44, 49, 59, 63, 74, 85, 99, 114, 126, 143, 166, 189, 221, 242, 277, 306, 351, 404, 447, 506, 565, 623, 710, 791, 899, 1021, 1150, 1268, 1364, 1533, 1734, 1949, 2149, 2386

Offset

0,4

Links

Table of n, a(n) for n=0..58.

Formula

a(n) + A241317(n) = A000009(n) for n >= 1.

Example

a(10) counts these 4 partitions:  {10,}, {5,4,1}, {5,3,2}, {4,3,2,1}.

Mathematica

z = 30; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241312 *)
    Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241313 *)
    Table[Count[f[n], p_ /; MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241314 *)
    Table[Count[f[n], p_ /; ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241315 *)
    Table[Count[f[n], p_ /; MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241316 *)
    Table[Count[f[n], p_ /; ! MemberQ[p, Round[Mean[p]]]], {n, 0, ] (* A241317 *)

Crossrefs

Cf. A241317, A241318, A000009.

Sequence in context: A127685 A127687 A024156 * A241312 A075989 A304714

Adjacent sequences: A241313 A241314 A241315 * A241317 A241318 A241319

Keyword

nonn,easy

Author

Clark Kimberling, Apr 19 2014

Status

approved