A240486 Number of partitions of n containing m(1) as a part, where m denotes multiplicity.

0, 1, 0, 1, 2, 2, 4, 5, 8, 10, 16, 19, 29, 36, 51, 63, 89, 108, 148, 182, 242, 297, 390, 475, 615, 750, 955, 1161, 1466, 1774, 2217, 2679, 3316, 3994, 4911, 5892, 7197, 8613, 10451, 12470, 15055, 17905, 21508, 25513, 30503, 36081, 42966, 50678, 60117, 70732

Offset

0,5

Links

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

Example

a(6) counts these 5 partitions:  51, 421, 331, 3211, 2221.

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. A240487 - A240490.

Sequence in context: A326631 A260894 A193146 * A237871 A027193 A126796

Adjacent sequences: A240483 A240484 A240485 * A240487 A240488 A240489

Keyword

nonn,easy

Author

Clark Kimberling, Apr 06 2014

Status

approved