A240490 - OEIS

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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

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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 *)