A240489 Number of partitions of n containing m(4) as a part, where m denotes multiplicity.

0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 7, 10, 14, 20, 27, 38, 52, 70, 93, 123, 161, 210, 272, 350, 447, 571, 722, 911, 1144, 1430, 1782, 2213, 2736, 3374, 4146, 5082, 6208, 7567, 9194, 11146, 13481, 16265, 19579, 23522, 28192, 33731, 40274, 47998, 57096, 67805, 80379

Offset

0,8

Links

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

Example

a(10) counts these 7 partitions:  541, 442, 4321, 43111, 42211, 421111, 4111111.

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, A240488, A240490.

Sequence in context: A062426 A184639 A035565 * A056513 A056518 A160644

Adjacent sequences: A240486 A240487 A240488 * A240490 A240491 A240492

Keyword

nonn,easy

Author

Clark Kimberling, Apr 06 2014

Status

approved