

A241546


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


3



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



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 *)
Table[Count[f[n], p_ /; MemberQ[p, s[1, p]]], {n, 0, z}] (* A241547 *)
Table[Count[f[n], p_ /; MemberQ[p, s[2, p]]], {n, 0, z}] (* A241548 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



