A241342 Number of partitions p of n such that floor(mean(p)) is a part and ceiling(mean(p)) is not.

0, 0, 0, 0, 0, 1, 1, 3, 4, 6, 9, 16, 11, 29, 36, 38, 51, 89, 81, 145, 134, 191, 278, 369, 290, 520, 678, 768, 875, 1320, 1161, 1961, 2009, 2624, 3453, 3733, 3650, 6131, 7244, 8187, 8097, 12563, 12301, 17770, 18725, 20962, 29260, 34902, 31199, 46507, 50889

Offset

0,8

Links

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

Example

a(10) counts these 9 partitions:  631, 6211, 532, 5221, 511111, 4222, 4111111, 331111, 31111111.

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, A241343, A241344.

Sequence in context: A332829 A173270 A301657 * A018830 A102934 A338061

Adjacent sequences: A241339 A241340 A241341 * A241343 A241344 A241345

Keyword

nonn,easy

Author

Clark Kimberling, Apr 20 2014

Status

approved