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A241546

Number of partitions p of n such that (number of numbers of the form 3k in p) is a part of p.

0, 0, 0, 0, 1, 1, 2, 4, 6, 9, 13, 20, 28, 39, 55, 75, 99, 136, 179, 237, 308, 403, 515, 666, 847, 1079, 1357, 1717, 2143, 2680, 3325, 4128, 5084, 6270, 7678, 9402, 11452, 13949, 16895, 20467, 24682, 29746, 35709, 42848, 51227, 61200, 72896, 86738, 102926

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OFFSET

0,7

COMMENTS

Each number in p is counted once, regardless of its multiplicity.

LINKS

Table of n, a(n) for n=0..48.

EXAMPLE

a(6) counts these 2 partitions: 321, 3111.

MATHEMATICA

z = 30; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k]

Table[Count[f[n], p_ /; MemberQ[p, s[0, p]]], {n, 0, z}] (* A241546 *)