A241335 Number of partitions p of n not including floor(mean(p)) as a part.

1, 0, 0, 0, 1, 1, 3, 4, 7, 9, 15, 18, 29, 36, 49, 65, 91, 108, 152, 184, 244, 311, 394, 473, 639, 772, 955, 1182, 1495, 1772, 2273, 2698, 3337, 4064, 4873, 5832, 7391, 8667, 10277, 12334, 15177, 17698, 21530, 25073, 30033, 36151, 42230, 48931, 59869, 69475

Offset

0,7

Links

Table of n, a(n) for n=0..49.

Example

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

Mathematica

z = 30; f[n_] := f[n] = IntegerPartitions[n];
    Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241334 *)
    Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]]], {n, 0, z}] (* A241335 *)
    Table[Count[f[n], p_ /; MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241336 *)
    Table[Count[f[n], p_ /; ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241337 *)
    Table[Count[f[n], p_ /; MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241338 *)
    Table[Count[f[n], p_ /; ! MemberQ[p, Round[Mean[p]]]], {n, 0, z}] (* A241339 *)

Crossrefs

Cf. A241334, A241336, A241338, A000041, A241312.

Sequence in context: A163468 A069183 A119907 * A158911 A086772 A301767

Adjacent sequences: A241332 A241333 A241334 * A241336 A241337 A241338

Keyword

nonn,easy

Author

Clark Kimberling, Apr 20 2014

Status

approved