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

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 *)
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

Cf. A241547, A241548.

Sequence in context: A143586 A363457 A344677 * A370320 A280918 A081225

Adjacent sequences: A241543 A241544 A241545 * A241547 A241548 A241549

Keyword

nonn,easy

Author

Clark Kimberling, Apr 26 2014

Status

approved