A241344 Number of partitions p of n such that floor(mean(p)) or ceiling(mean(p)) is a part.

0, 1, 2, 3, 4, 6, 8, 12, 16, 22, 31, 44, 50, 78, 102, 125, 163, 230, 271, 379, 441, 575, 760, 978, 1073, 1457, 1865, 2250, 2704, 3544, 3955, 5293, 6154, 7637, 9533, 11171, 12702, 16718, 20215, 23926, 26949, 34725, 39187, 49415, 56914, 66105, 82244, 98231

Offset

0,3

Links

Table of n, a(n) for n=0..47.

Example

a(6) counts these 8 partitions:  6, 33, 321, 3111, 222, 21111, 111111.

Mathematica

z = 30; f[n_] := f[n] = IntegerPartitions[n];
    t1 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241340 *)
    t2 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241341 *)
    t3 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241342 *)
    t4 = Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241343 *)
    t5 = Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] || MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241344 *)

Crossrefs

Cf. A241340, A241341, A241342, A241343.

Sequence in context: A005987 A241828 A125895 * A064428 A052810 A364964

Adjacent sequences: A241341 A241342 A241343 * A241345 A241346 A241347

Keyword

nonn,easy

Author

Clark Kimberling, Apr 20 2014

Status

approved