A241341 Number of partitions p of n such that ceiling(mean(p)) is a part and floor(mean(p)) is not.

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 4, 6, 2, 13, 16, 14, 23, 41, 38, 73, 58, 94, 152, 196, 137, 271, 384, 422, 481, 751, 624, 1149, 1142, 1558, 2096, 2120, 2116, 3748, 4477, 5075, 4788, 7840, 7543, 11227, 11772, 13122, 18916, 22408, 19619, 29862, 32604, 41688

Offset

0,11

Links

Table of n, a(n) for n=0..51.

Example

a(10) counts these 4 partitions:  541, 5311, 442, 3331.

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, A241342, A241343, A241344.

Sequence in context: A059030 A066984 A364724 * A085595 A173458 A054222

Adjacent sequences: A241338 A241339 A241340 * A241342 A241343 A241344

Keyword

nonn,easy

Author

Clark Kimberling, Apr 20 2014

Status

approved