A241321 Number of partitions p of n into distinct parts, including neither floor(mean(p)) nor ceiling(mean(p)).

0, 0, 0, 0, 1, 1, 2, 2, 3, 4, 5, 5, 10, 8, 11, 15, 19, 18, 27, 26, 40, 43, 46, 51, 79, 80, 86, 104, 131, 130, 190, 177, 228, 241, 264, 349, 428, 403, 454, 520, 709, 663, 880, 856, 1019, 1230, 1224, 1360, 1833, 1863, 2167, 2216, 2531, 2710, 3434, 3696, 4407

Offset

0,7

Links

Table of n, a(n) for n=0..56.

Formula

a(n) + A241322(n) = A000009(n) for n >= 1.

Example

a(11) counts these 5 partitions:  {10,1}, {9,2}, {8,3}, {8,2,1}, {7,4}.

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, A241320, A241322, A241312, A000009.

Sequence in context: A332285 A324325 A318284 * A093936 A329904 A331307

Adjacent sequences: A241318 A241319 A241320 * A241322 A241323 A241324

Keyword

nonn,easy

Author

Clark Kimberling, Apr 19 2014

Status

approved