A241322 Number of partitions p of n into distinct parts, including floor(mean(p)) or ceiling(mean(p)).

0, 1, 1, 2, 1, 2, 2, 3, 3, 4, 5, 7, 5, 10, 11, 12, 13, 20, 19, 28, 24, 33, 43, 53, 43, 62, 79, 88, 91, 126, 106, 163, 162, 207, 248, 236, 240, 357, 410, 462, 404, 597, 546, 754, 797, 818, 1080, 1230, 1077, 1401, 1491, 1881, 2051, 2410, 2284, 2682, 2701, 3609

Offset

0,4

Links

Table of n, a(n) for n=0..57.

Formula

a(n) + A241321(n) = A000009(n) for n >= 1.

Example

a(11) counts these 7 partitions:  {11}, {7,3,1}, {6,5}, {6,4,1}, {6,3,2}, {5,4,2}, {5,3,2,1}.

Mathematica

z = 30; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && 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, A241321, A241312, A000009.

Sequence in context: A214130 A029172 A240864 * A275380 A161052 A161256

Adjacent sequences: A241319 A241320 A241321 * A241323 A241324 A241325

Keyword

nonn,easy

Author

Clark Kimberling, Apr 19 2014

Status

approved