A241320 Number of partitions p of n into distinct parts, including floor(mean(p)) but not ceiling(mean(p)).

0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 4, 4, 2, 4, 8, 5, 12, 5, 10, 19, 22, 8, 21, 34, 34, 29, 54, 21, 72, 57, 83, 109, 70, 59, 158, 179, 195, 99, 259, 160, 332, 317, 270, 471, 537, 286, 542, 537, 816, 852, 1051, 751, 995, 828, 1584, 1789, 2005, 941, 2431

Offset

0,11

Links

Table of n, a(n) for n=0..61.

Example

a(11) counts these 2 partitions:  641, 542.

Mathematica

z = 30; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241318 *)
    Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241319 *)
    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241320 *)
    Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241321 *)
    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] || MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241322 *)

Crossrefs

Cf. A241318, A241319, A241321, A241322, A241312, A000009.

Sequence in context: A078030 A262056 A264628 * A073469 A307076 A342472

Adjacent sequences: A241317 A241318 A241319 * A241321 A241322 A241323

Keyword

nonn,easy

Author

Clark Kimberling, Apr 19 2014

Status

approved