A241343 Number of partitions p of n such that neither floor(mean(p)) nor ceiling(mean(p)) is a part.

1, 0, 0, 0, 1, 1, 3, 3, 6, 8, 11, 12, 27, 23, 33, 51, 68, 67, 114, 111, 186, 217, 242, 277, 502, 501, 571, 760, 1014, 1021, 1649, 1549, 2195, 2506, 2777, 3712, 5275, 4919, 5800, 7259, 10389, 9858, 13987, 13846, 18261, 23029, 23314, 26523, 40250, 39613, 49286

Offset

0,7

Links

Table of n, a(n) for n=0..50.

Example

a(6) counts these 3 partitions:  51, 42, 411.

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, A241344.

Sequence in context: A160733 A021752 A049626 * A309455 A168637 A372887

Adjacent sequences: A241340 A241341 A241342 * A241344 A241345 A241346

Keyword

nonn,easy

Author

Clark Kimberling, Apr 20 2014

Status

approved