A240487 Number of partitions of n containing m(2) as a part, where m denotes multiplicity.

0, 0, 0, 1, 2, 2, 3, 5, 7, 11, 15, 20, 29, 39, 51, 70, 92, 119, 157, 203, 259, 334, 424, 535, 678, 850, 1059, 1324, 1642, 2027, 2503, 3075, 3763, 4604, 5607, 6809, 8261, 9988, 12043, 14508, 17424, 20879, 24988, 29835, 35548, 42303, 50232, 59544, 70491, 83297

Offset

0,5

Links

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

Example

a(7) counts these 5 partitions:  421, 322, 3211, 22111, 211111.

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 1]]], {n, 0, z}] (* A240486 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2]]], {n, 0, z}] (* A240487 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 3]]], {n, 0, z}] (* A240488 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 4]]], {n, 0, z}] (* A240489 *)
Table[Count[f[n], p_ /; MemberQ[p, Count[p, 5]]], {n, 0, z}] (* A240490 *)

Crossrefs

Cf. A240486 - A240490.

Sequence in context: A322429 A039894 A133225 * A066889 A214040 A077419

Adjacent sequences: A240484 A240485 A240486 * A240488 A240489 A240490

Keyword

nonn,easy

Author

Clark Kimberling, Apr 06 2014

Status

approved