A241547 Number of partitions p of n such that (number of numbers of the form 3k+1 in p) is a part of p.

0, 1, 1, 2, 3, 4, 6, 10, 12, 18, 25, 33, 45, 63, 77, 107, 139, 177, 231, 302, 372, 486, 612, 762, 969, 1214, 1489, 1879, 2315, 2839, 3522, 4318, 5243, 6460, 7835, 9483, 11558, 13938, 16763, 20285, 24302, 29087, 34941, 41642, 49588, 59198, 70199, 83205, 98780

Offset

0,4

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 6 partitions:  51, 321, 3111, 2211, 21111, 111111.

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. A241546, A241548.

Sequence in context: A288784 A322164 A237823 * A273542 A061018 A130126

Adjacent sequences: A241544 A241545 A241546 * A241548 A241549 A241550

Keyword

nonn,easy

Author

Clark Kimberling, Apr 26 2014

Status

approved