A240488 Number of partitions of n containing m(3) as a part, where m denotes multiplicity.

0, 0, 0, 0, 1, 1, 2, 2, 5, 7, 11, 14, 21, 28, 40, 52, 73, 94, 127, 162, 216, 274, 357, 449, 579, 724, 920, 1142, 1439, 1777, 2216, 2720, 3368, 4114, 5056, 6144, 7506, 9081, 11028, 13284, 16052, 19259, 23157, 27677, 33139, 39467, 47060, 55854, 66355, 78506

Offset

0,7

Links

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

Example

a(8) counts these 5 partitions:  431, 332, 3221, 32111, 311111.

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, A240487, A240489, A240490.

Sequence in context: A259446 A265769 A308957 * A238491 A326449 A326529

Adjacent sequences: A240485 A240486 A240487 * A240489 A240490 A240491

Keyword

nonn,easy

Author

Clark Kimberling, Apr 06 2014

Status

approved