A241548 Number of partitions p of n such that (number of numbers of the form 3k+2 in p) is a part of p.

0, 0, 0, 1, 1, 2, 4, 7, 8, 15, 21, 29, 42, 60, 76, 107, 144, 186, 246, 326, 409, 532, 683, 856, 1083, 1374, 1698, 2121, 2644, 3244, 3998, 4930, 5995, 7316, 8927, 10782, 13043, 15778, 18932, 22729, 27289, 32549, 38833, 46316, 54951, 65172, 77290, 91239

Offset

0,6

Comments

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

Links

Table of n, a(n) for n=0..47.

Example

a(6) counts these 4 partitions:  51, 321, 2211, 21111.

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, A241547.

Sequence in context: A018265 A056694 A090606 * A019539 A327099 A338888

Adjacent sequences: A241545 A241546 A241547 * A241549 A241550 A241551

Keyword

nonn,easy

Author

Clark Kimberling, Apr 26 2014

Status

approved