A240490 Number of partitions of n containing m(5) as a part, where m denotes multiplicity.

0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 6, 11, 14, 21, 28, 40, 51, 73, 93, 126, 162, 215, 271, 357, 449, 578, 725, 923, 1146, 1447, 1788, 2232, 2747, 3403, 4160, 5123, 6234, 7620, 9236, 11227, 13540, 16381, 19678, 23682, 28348, 33969, 40501, 48346, 57449, 68302

Offset

0,9

Links

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

Example

a(12) counts these 11 partitions:  651, 552, 5421, 54111, 5331, 53211, 531111, 52221, 522111, 5211111, 51111111.

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, A240489.

Sequence in context: A132581 A238542 A184640 * A039839 A039844 A276107

Adjacent sequences: A240487 A240488 A240489 * A240491 A240492 A240493

Keyword

nonn,easy

Author

Clark Kimberling, Apr 06 2014

Status

approved