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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

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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 *)