A241319 Number of partitions p of n into distinct parts, including ceiling(mean(p)) but not floor(mean(p)).

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 3, 4, 1, 3, 7, 4, 9, 5, 8, 15, 19, 6, 18, 30, 27, 25, 46, 19, 61, 48, 73, 92, 62, 51, 136, 158, 168, 83, 228, 142, 293, 276, 232, 417, 471, 255, 483, 470, 725, 746, 938, 663, 879, 752, 1407, 1601, 1789, 814, 2172, 2431

Offset

0,12

Links

Table of n, a(n) for n=0..62.

Example

a(11) counts these 2 partitions:  731, 632.

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, A241320, A241321, A241322, A000009.

Sequence in context: A212844 A066439 A352579 * A287016 A368312 A285722

Adjacent sequences: A241316 A241317 A241318 * A241320 A241321 A241322

Keyword

nonn,easy

Author

Clark Kimberling, Apr 19 2014

Status

approved