A241312 Number of partitions p of n into distinct parts, including floor(mean(p)).

0, 1, 1, 2, 1, 2, 2, 3, 2, 4, 4, 5, 5, 7, 7, 11, 10, 13, 15, 19, 19, 25, 28, 34, 37, 44, 49, 61, 66, 80, 87, 102, 114, 134, 156, 174, 189, 221, 252, 294, 321, 369, 404, 461, 521, 586, 663, 759, 822, 918, 1021, 1156, 1305, 1472, 1621, 1803, 1949, 2202, 2469

Offset

0,4

Links

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

Formula

a(n) + A241313(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. A241313, A241314, A241315, A241318, A000009.

Sequence in context: A127687 A024156 A241316 * A075989 A304714 A085432

Adjacent sequences: A241309 A241310 A241311 * A241313 A241314 A241315

Keyword

nonn,easy

Author

Clark Kimberling, Apr 19 2014

Status

approved